STUDY OF RADIOACTIVITY AND MEASUREMENT

OF ABSORPTION COEFFICIENT OF GAMMA RAYS

OF PHOTONS FOR ALANINE

Submitted to

Dr. Babasaheb Ambedkar Marathwada University,

Aurangabad

Submitted By Mr. Haqi Esmail Shareef

Under the guidance of Dr. Pravina Pawar

Department of Physics,Dr. Babasaheb Ambedkar Marathwada University,

Aurangabad

1

Certificate This is to certify that Mr. Haqi Esmail Shareef has successfully

completed the project intitled “Study of Radioactivity and Measurement

Of absorption Coefficient of Gamma Rays of Photons for Alanine”

under the guide of Dr. K.M. Jadhav and Pravina Pawar.

For partial fulfillment of requirement for a work of the degree of

Master of Science in Physics with specialization Nuclear Physical in the

Academics year 2011-2012.

2

Prof. (Dr) K.M. Jadhav

(Professor Incharge)

Dr. Pravina Pawar

(Asst. Professor)

Prof. (Dr) P.W. Khirade

Examiner

AcknowledgmentI express my first and for most thanks and gratitude to Prof. Dr.

K.M. Jadhav Sir for permitting me to undertake this project work and

giving valuable guidance. He has a source of inspiration for completion

and shaping of the assigned work in a proper way. If feel honored to

remain indebted to him forever…

It is also a pleasure to express my gratitude thanks to Dr. Pravina

Pawar mam, for giving a valuable guidance. Her affective concern,

proper guidance, and inspiring nature naturally turned me towards the

fulfillment of my project… I also express thanks to my father and mother

and wife and two sons who directly helped and supported me all time.

Haqi Esmail Shareef

M.Sc. Physics(Nuclear Physics)

3

INDEXSr. No. Chapter Name Sr. No.

I Introduction 5-32Historical Introduction 5

Radioactivity 5-6

Definition of Radioactivity 6

Natural Radioactivity 7

Artificial Radioactivity 7

Units of Radioactivity 7

Types of decay 10

Activity measurements 12

Mathematics of radioactive decay 12

Universal law of radioactive decay 13

One –decay process 13

Glossary 14

Application of radioactivity 17

Nuclear medicine 17

Radiotherapy 18

Radioactive tracers 18

Industry and the Home 18

Power Generation 20

Art Restoration 20

Fundamental Laws Of Radioactivity 24

Radioactive decay series 29

II Introduction to biomolecule 33-54

4

Biomolecules 33

Importance of Biomolecules 33

Type of Biomolecules 34

Biomolecule - Amino - Acids 35

Amino acid - General Structure 38

Functional Significance of Amino Acid R-Groups

38

General Properties 39

Peptide Bonds 39

Classification 40

Physical Properties 42

Optical Properties of the Amino Acids 45

Chemical Nature of the Amino Acids 45

Acid-Base Properties of the Amino Acids 48

Amino Acid Benefits 49

Amino acids and their functions in the body 50

III Cross section 55-69

Gamma radiation 57

Absorption coefficient of Gamma ray photons

59

interaction of gamma ray photon with matter 61

IV Result & Discussion 88

V Conclusions 88-89

References 90-91

5

CHAPTER - I

INTRODUCTION

HISTORICAL INTRODUCTION

In attempting to discover a possible connection between X-rays

and luminescence observed in a discharge tube, H. Becquerel (1895)

found that after exposure to cathode rasy potassium suranyl sulfate

possessed the property of affecting a photographic plate wrapped in black

paper, indicating that the uranium salt was emitting a penetrating type of

radiation. In the same year he made surprising discovery that uranium

compounds alone, without any previous treatment, are capable of fogging

a photographic plate, and so emit rays spontaneously. In addition to their

photographic action, the radiations were foud, like X-rays, to be capable

of ionizing the year, so that the activity of a uranium compound could be

measured by the rate at which a known quantity caused the discharged of

an electroscope. The emission of rays capable of producing these effects

is a fundamental property of the uranium atom, as the rays are observed

with various uranium salts in different valence states as well as with the

element itself; further, the activity is found to be independent of the

temperature or previous history of the material. The spontaneous

emission of radiation of this type is now known as

Radioactivity:

A study of the subject has thrown much light on the structure of

matter.

When examining the ionizing activity of the mineral pitchblende,

one of the chief ores of uranium and consisting mainly of U3O8 Mme. M.

Curie and her husband, P Curie (1898) Noted that it had a greater activity

than was expected from the uranium it contained. This result indicated the

6

presence in the ore of compounds an element, or elements, even more

radioactive than uranium and by using ordinary chemical methods of

separation, two such substances were isolated. One of the elements was

precipitated as its sulfide with bismuth sulfide; it was called polonium, in

honor of Poland, the native country of Mme. Curie. The other elements

separated together with barium as their sulfates, which were subsequently

converted the bromides and separated by fraction crystallization. The

elements, obtained as the impure bromide by M. Curie, P. Curie and G.

Bemont (1898), was given the name Radium because of exceptional

activity. After wards, A Debierne (1899) and F. Giesel (1901) found the

new radioelement actinium in uranium minerals.

In the course of a study of the penetrating power of the radiations.

Rutherford (1899) Concluded that they could be divided in to two types,

which he referred to as α-rays and β-Rays, Respectively.

Shortly afterwards P Curie Founded that part of radiation was not

deflected in a magnetic field, and this was shown by P. Villard to have

exceptional penetrating power, these radiations were called the γ-rays.

Definition of Radioactivity:

The phenomenon of spontaneous disintegration of an unstable

atomic nucleus accompanied by emission of radiation is called

radioactivity.

Radioactivity was discovered by Henry Becquerel in 1896. He

found that photographic plate was affected when placed near uranium

salt. He concluded that the Uranium might have emitted highly entreating

and invisible radiation. Later Madam Curic was confirmed the same. The

substances showing this property are called radioactive substances.e.g. U,

Ra, Th.

7

Natural Radioactivity:

The phenomenon of spontaneous emission of highly penetrating

and invisible radiation from heavy element is called natural radioactivity.

It is generally shown by heavy element having atomic number 83 or more

than that.

Artificial Radioactivity:

The process of stable nucleus into unstable radioactive nucleus by

bombarding it with suitable projectile is called artificial radioactivity.

It is generally shown by light element having atomic number less

than 83.

Units of Radioactivity:

In general, radiation is in the form of an alpha- particle (i.e.,

ionized helium atom having two units of positive charge and four units of

mass), a beta-ray (a particle of mass equal to that of an electron and of

either positive or negative charge emitted from a nucleus due to the

proton or neutron decay), a gamma –ray an electromagnetic radiation

similar to X-rays but emanating from a nucleus) and neutrons. A

radioactive material is characterized by the type of radiation it emits, the

energy of the emitted radiation, and its half.

Half –life is the time required for reducing the number of

radioactive to one-half the initial value. Some of the naturally

occurring radioisotopes have a very long half- life [in the range of

thousands of years (yr), whereas some artificially produced radioisotopes

have a very short half- life [ in the range of milliseconds (msec) to

microseconds (sec) ] Thus it is essential that we define the activity or

8

disintegration rat e of a radioisotope since each disintegration emits an

energetic particle which interacts with the surrounding medium.

The fundamental unit of radioactivity is the curie (Ci). One curie

represents 3.7 × 1010 disintegrations per second (dis/sec) of any type of

radiation. This unit has now been replaced by an SI unit, called the

Becquerel (Bq), which represents one disintegration per second. As is

evident, the Becquerel is itself a small unit. The conventionally used

units, smaller than the curie, are known as milicurie (mCi; 1 mCi = 10 -3

Ci) and microcurie (µCi; 1µCi =10-6 Ci) Most sources handled in a

laboratory are either of microcurie or, at the most, few millicurie strength.

The radioisotopes used in food processing and medical therapy can be of

the order of several kilocurie (kCi) or even megacurie (MCi)

If N represents the number of atoms of a radioactive substance and

its disintegration rate constant or decay constant (ie., probability of

disintegrations per second per atom) hen the product N … represents the

activity of the substance. The disintegration rate constant is related to half

life T ½ as 0.693/ T1/2 since, at any time t,N(t) Noe-. Therefore, for a

given N, a substance with a long half – life will be less active than a

substance with a short half- life. Thus, an optimal choice of weight and

half –life is always desirable, depending on the situation. Some of

radioisotopes commonly used in the laboratory and their radiations are

indicated in Fig 1.1 and Table 1.1.

9

Table 1.1 Some common laboratory radioactive sources

(a) Gamma –ray Sources

Isotope Half life Gamma –ray energy

(Mev)137 Cs60Co

22 Na

54Mn88 Y

30 yr

5.25 yr

2.6 yr

300d

108d

0.662 (93.5%)

1.173 (100%)

1.332(100%)

1.275 (100%)

0.511 (100%)

0.835 (100%)

0.898 (91%)

1.836%)

Table 1.1 Some common laboratory radioactive sources

(b)Beta-ray sources ( negative)

Isotope Half life Maximum energy

(Mev)99 Tc14C3H204 TI147 PM35S32P90Sr/ 90Y

2.12 × 105 yr

5730 yr

12.26 yr

3.81 yr

2.62 yr

87.9 d

14.28d

27.7yr /64 hr

0.292

0.156

0.0186

0.766

0.224

0.167

1.71

0.56/2.27

10

Example Calculate the activity of 1 gm of radium, 226 Ra, whose half life

is 1620 yr.

One gram of radium contains (6.203 × 1023)/226 atoms. The decay

constant of radium is.

0.693 0.693= yr -1 = 1620 1620 yr × 365 d/yr × 24 hr /d × 3600 s ec.3/ hr

Types of decay

As for types of radioactive radiation, it was found that an electric

or magnetic field could split such emissions into three types of beams.

For lack of better terms, the rays were given the alphabetic names alpha,

beta and gamma, still in use today. While alpha decay was seen only in

heavier elements (atomic number 52, tellurium and greater), the other two

types of decay were seen in all of the elements.

In analyzing the nature of the decay products, it was obvious from

the direction of electromagnetic forces produced upon the radiations by

external magnetic and electric fields that alpha rays carried a positive

charge, beta rays carried negative charge, and gamma rays were neutral.

From the magnitude of deflection, it was clear that alpha particles were

much more massive than beta particles. Passing alpha particles through a

very thin glass window and trapping them in a discharge tube allowed

researchers to study the emission spectrum of the resulting gas, and

ultimately prove that alpha particles are helium nuclei. Other experiments

showed the similarity between classical beta radiation and cathode rays.

They are both streams of electrons. Likewise gamma radiation and x-rays

were found to be similar high – energy electromagnetic radiation.

11

Although alpha, beta, and gamma were found most commonly,

other types of decay were eventually discovered. Shortly after the

discovery of the positron in cosmic ray products, it was realized that the

same process that operates in classical beta decay can also produce

positrons. (Positron emission). In an analogous process, instead of

emitting positrons and neutrinos, some proton-rich nuclides were found to

capture their own atomic electrons (electron capture) and emit only a

neutrino (and usually also a gamma ray). Each of these types of decay

involves the capture or emission of nuclear electrons or positrons, and

acts to move a nucleus toward the ratio. Some radionuclides may have

several different paths of decay. For example, approximately 36% of

bismuth decays, through alpha –emission, to thallium -208 while

approximately 64% of bismuth 212 decays, through beta – emission to

polonium -212. Both thallium-208 and the polonium-212 is radioactive

daughter of bismuth -212. And both decay directly to stable lead -208.

Constant quantities

The half –life – T ½, is the lime taken for the activity of a given

amount of a radioactive substance to decay to half of its initial

value.

The mean lifetime- T, “tau” the average lifetime of radioactive

particle before decay.

The decay constant - lambda” the inverse of the mean lifetime.

Although these are constants, they are associated with statistically

random behavior of populations of atoms. In consequence predictions

using these constants are less accurate for small number of atoms.

In principle the reciprocal of any number greater than one- half life,

third life or even a ( 1/2- life – can be used in exactly the same way as

12

half –life , but the half – life t ½ is adopted as the standard time associated

with exponential decay.

Time- variable quantities:

Total activity – A is number of decays per unit time of a

radioactive sample.

Number of particles – N is the total number of particles in

the sample.

Specific activity – SA, number of decays per unit time per

amount of substance of the sample at time set to Zero (t=0)

Amount of substance can be the mass, volume or moles of the

initial sample.

These are related as follows

Where α0 is the initial amount of active substance- substance that has the

same percentage of unstable particles as when the substance was formed.

Activity measurements

The units in which activities are measured are becqurel (symbol

Bq) = one disintegration per second, curie (Ci) = 3.7×1010 Bq. Low

activities are also measured in disintegrations per minute (dpm).

Mathematics of radioactive decay

For the mathematical details of exponential decay in general

context, see exponential decay for related derivations with some further

details, see half –life.

For the analogous mathematics in 1st order chemical reactions, see

consecutive reactions.

13

Universal law of radioactive decay

Radioactivity is one very frequent example of exponential decay.

The law however is only statistical – not exact. In the following

formalism, the number of nuclides or nuclide population N, is of course a

discrete variable ( a natural number) but for any physical sample N is so

large (amounts of L =1023 Avogadro’s constant) that it can be treated as

a continuous variable. Differential calculus to set up differential equations

for modeling the behavior of the nuclear decay.

One –decay process

Consider the case of a nuclide a decaying into another B by some

process A B (emission of other particles, like electron neutrinos V.

E and electrons e in beta decay are irrelevant in what follows). The

decay of an unstable nucleus is entirely random and it is impossible to

predict when a particular atom will decay. However it is equally likely to

decay at any time. Therefore, given a sample of a particular radioisotope,

the number of decay events – d/ N expected to occur in a small interval

of time d/ is proportional to the number of atoms present N that is.

Particular radionuclides decay at different rates, so each has its

own decay constant they probability of decay – dN/* N is proportional

to an increment of time df.

The negative sign indicates that N decrease as time increases, as

each decay event follows one after another. The solution to this first order

differential equation is the function.

Where N0 is the value of N at time t = 0

14

This equation is of particular interest; the behavior of numerous

important quantities can be found from it (see below). Although the

parent decay distribution follows an exponential, observations of decay

times will be limited by a finite integer number of N atoms and follow

Poisson statistics as a consequence of t he random nature of the process.

We have for all time t:

NA + NB = N total = N A0,

Where Ntotal is the constant number of particles throughout the

decay process, clearly equal to the initial number of nuclides since this is

the initial substance.

If the number of non –decayed A nuclei is: Then the number of

nuclei of B, i.e. number of decayed a nuclei, is

Glossary :

Important terms used in connection with radioactivity are given

below; the terms given do not necessarily appear in the present article.

Alpha particle: charged particles emitted from a radioactive atom.

Each charged particle consists of two protons and two neutrons. Atom:

This is the smallest unit of an element. It contains a nucleus with neutrons

and protons, surrounded by orbiting electrons. Atomic mass: the mass of

an atom usually expressed as atomic mass unit (amu).

Beta particle: (often designated beta rays) charged particles emitted from

a radioactive atom. These particles are identical except for their charge.

The charge is classified as positive (positron) or negative (electrons or

negatron).

15

Carbon 14: A naturally occurring radio isotope of carbon having a mass

number of 14 and half life 5780 years. Used in Radio carbon dating for

determination of age of ancient objects.

Cathode ray: Electrons originating at the cathodes of gaseous discharge

devices.3 these electrons are often focused in a small area such as a tube

and intensified on a surface. The most familiar form of a cathode- ray

tube is the television picture tube.

Conductivity: The ratio of electric current to the field in a material.

Passage of electric charger which can be occur a variety of ways such as

passage of electrons or ionized atoms.

Curie: A unit of radioactivity, defined as that quantity of any radioactive

nuclide which has 3700 x 1010 disintegrations per second.

Deuterium: The isotope of element hydrogen with one neutron and one

proton in his nucleus.

Electrons: A negative charged particle that orbits the nucleus of an atom.

It is lighter in weight than a proton or neutron.

Elements: An element is a substance made up of atoms with the same

atomic number. 75% of the elements are metals and the others are

nonmetals. A few examples are oxygen, iron, gold, chlorine, and

uranium.

Fluorescence: Electrons absorb energetic radiation (for example

ultraviolet light) raising an electron to a higher “Bohr” orbit. The

energized electron soon drops down in a series of steps through lower

energy states and in the process release photons at lower energy stares

corresponding to visible light. The bright color occurs because the

photons are concentrated in a narrow range of wavelengths.

16

Geiger counter : A radiation counter that uses a Geiger – Muller tube in

appropriate circuits to detect and count ionizing particles , each particle

crossing the tube produces ionization of gas in the tube which is roughly

independent of the particle’s nature and energy resulting a uniform

discharge across the tube. Also knows as Geiger – Muller counter.

Geiger Muller tube: A radiation counter tube usually consisting of a gas

–filled cylindrical metal chamber containing a fine –wire anode at its

axis. Also knows as Geiger – Muller Counter tube.

Half –life: The period of time in takes for half the nuclei of a radioactive

element to undergo decay to another nuclear form.

Heavy water: A compound of hydrogen and oxygen containing a higher

proportion of the hydrogen isotope deuterium, than does naturally

occurring water.

Ionization chamber: A particle detector which measures the ionization

produced in the gas filling the chamber by the fast moving charged

particles as they pass through.

Isotope: Atoms having the same number of protons in its nucleus as other

varieties of the element but has a different number of neutrons.

Magnetic field: All magnetic fields are created by moving electric

charge. The single moving electron around a nucleus is a tiny electric

current. These orbiting electrons create magnetic fields and their net

effect is to provide the atom with a magnetic field.

Neutron: A particle with no charge that is located in the nucleus of an

atom.

17

Nuclear physics: A branch of physics that includes the study of the

nuclei of atoms, their interactions with each other, and with constituent

particles.

Nucleus: The central part of every atom that contains protons and

neutrons.

Nuclide: A species of atom characterized by the number of protons,

number, and energy content in the nucleus, or alternatively by the atomic

number, mass number and atomic mass. To be regarded as a district

nuclide, the atom must be capable of existing for a measurable life time.

Also knows as nuclear species.

Application of radioactivity:

The principles of radioactivity and radioactivity decay have wide –

ranging applications in medicine, industry, the home, the arts and

sciences, and electric power generation.

Nuclear medicine:

Nuclear medicine is a branch of medicine and medical imaging that

uses the nuclear properties of matter in diagnosis and therapy. Many

procedures in nuclear medicine use pharmaceuticals that have been

labeled with radionuclides (radiopharmaceuticals). In diagnosis,

radioactive substances are administered to patients and the radiation

emitted is measured. The majority of these diagnostic tests involve the

formation of an image using a gamma camera. Imaging may also be

referred to as radionuclide imaging or nuclear scintigraphy. Other

diagnostic tests use probes to acquire measurements from parts of the

body, or counters for the measurement of samples taken from the patient.

In therapy, radionuclides are administered to treat disease or provide

18

palliative pain relief. For example, administration of Iodine -131 is often

used for the treatment of thyrotoxicosis and thyroid cancer.

Radiotherapy

Radiation therapy (or radiotherapy) is the medical use of ionizing

radiation as part of cancer treatment to control malignant cells. The

radiation may be given in the form of external beam radiotherapy of high

– energy electrons or X-rays or it may come from radioactive sources

placed inside the patient.

Radioactive tracers

Radioactive tracers are radioactive substances added in minute

amounts to the reacting elements or compounds in a chemical process and

traced through the process by appropriate detection methods, e.g. Geiger

counter. Compounds containing tracers are often said to be tagged or

labeled.

In medical applications, a radioactive atom can be attached to a

molecule or more complex substance, which can then be used to examine

a chemical reaction in a test tube, or it can be administered to a patient by

ingestion or injection and subsequently be incorporated into a

biochemical process. The radioactive emissions from the radioactive

atom can be used to track the behavior of the labeled molecule or

substance in biological process by means of medical imaging.

Industry and the Home

Radiation processing is the use of ionizing radiation to produce

beneficial physical chemical or biological effects on an industrial scale.

Examples include.

19

The isotope 252Cf (a neutron emitter) is used in neutron activation

analysis to inspect airline luggage for hidden explosives, to gauge

the moisture content of soil and other materials, in bore hole

logging in geology, and in human cervix cancer therapy.

In paper mills, the thickness of the paper can be controlled by

measuring how much beta radiation passes through the paper to a

Geiger counter. The counter controls the pressure of the rollers to

give the correct thickness.

Checking Welds. If a gamma source is placed on one side of the

welded metal, and a photographic film on the other side, weak

points or air bubbles will show up on the film.

Foodstuffs can be irradiated to extend shelf life or reduce the

numbers of harmful bacteria.

Improve material properties, particularly in polymers, curing

adhesives and resins, improvement of gemstones, wire and cable

jacket curing, tire manufacture.

Smoke alarms contain a weak source made of Americium -241.

Alpha particles are emitted that ionize the air, so that the air

conducts electricity and a small current flow. If smoke enters the

alarm, this absorbs the particles, the current reduces and the

alarm sounds.

Radiation has many uses in agriculture. In plant research, radiation

is used to develop new plant types to speed up the process of developing

superior agricultural products. Insect control is another important

application; pest populations are drastically reduced and, in some cases,

eliminated by exposing male insects to sterilizing doses of radiation.

Fertilizer consumption has been reduced through research with

radioactive tracers. Radiation pellets are used is grain elevators to kill

20

insects and rodents. Irradiation prolongs the shelf- life of foods by

destroying bacteria, viruses and molds.

Radioactive dating

Radioactive dating or radiometric dating is a technique used to date

materials based on knowledge of the decay rates of naturally occurring

isotopes, and their current abundances. Many isotopes have been studied,

probing a wide range of time scales. Radioactive dating is the principal

source of information about the age of the Earth and rates of evolutionary

change and is used to estimate the age of once- living materials.

Power Generation

Nuclear power is a type of nuclear technology involving the

controlled used of nuclear fission to release energy for work including

propulsion, heat and the generation of electricity. Nuclear energy is

produced by a controlled nuclear chain reaction and creates heat which is

used to boil water, produce steam and drive a steam turbine. The turbine

can be used for mechanical work and also to generate electricity. As of

2007, nuclear power provided about 6% of the world’s energy and 16%

of the world’s electricity with the U.S. France, and Japan together

accounting for 57% of all nuclear generated electricity.

Art Restoration

Nuclear science plays an important role in the art world. A

technique known as X-ray fluorescence spectroscopy (or XRF) works by

irradiating samples of materials using X-rays without destroying the

analyzed material. At the same time, it can identify a vast number of

21

elements simultaneously, making it an excellent way to “fingerprint” all

kinds of materials. For example, XRF has been used to examine the tip of

David’s nose, analyzing dust and dirt before Michelango’s masterpiece

could be safely restored.

Restration work on Cellini’s bronze statue of Perseus at the Uffizi

Museum in Florence also benefited from insights gained using XRF.

Examinations of Perseus right knee showed that the bronze alloy was

composed of varying percentages of copper, tin lead, antimony, iron and

silver.

Clues from XRF results also can aid forensic scientists in solving

crimes; for example, by determining if a paint pigment matches the artist

original palette. Discovering the presence of a modern replacement for an

old traditional pigment known to be used by a particular artist can provide

evidence that a painting is a forgery.

Common Radioisotopes and Their Uses

Americium – 2141 : Used in many smoke detectors for homes and

business to measure levels of toxic lead in dried paint samples , to ensure

uniform thickness in rolling processes like steel and paper production,

and to help determine where oil wells should be drilled.

Cadmium 109: Used to analyze metal alloys for checking stock and

sorting scrap.

Californium -252: Used to measure the mineral content of coal ash and

to measure the moisture of materials stored in silos.

Carbon -14: Used in research to ensure that potential new drugs are

metabolized without forming harmful by products.

22

Cesium 137 : Used to treat cancers ; to calibrate the equipment used to

measure correct patient dosages of radioactive pharmaceuticals; to

measure and control the liquid flow in oil pipelines; to tell researchers

whether oil wells are plugged by sand; and to ensure the right fill level

for packages of food, drugs and other products. (The products in these

packages do not become radioactive).

Chromium -51: Used in research in red blood cell survival studies.

Cobalt -57: used in nuclear medicine to help physicians interpret

diagnostic scans of patients organs and to diagnose pernicious anemia.

Cobalt 60: Used to sterilize surgical instruments: to improve the safety

and reliability of industrial fuel oil burners: and to preserve poultry, fruits

sand spices.

Copper 67: When injected with monoclonal antibodies into a cancer

patient. Helps the antibodies bind to and destroy the tumor.

Curium 244: Used in mining to analyze material excavated from pits and

slurries from drilling operations.

Iodine 131: Used to diagnose and treat thyroid disorders.

Iridium 192: Used to test the integrity of pipeline welds boilers and

aircraft parts.

Iron 55: Used to analyze electroplating solutions.

Krypton 85 : Used in indicator lights in appliances like clothes of thin

plastics sheet metal washers and dryers, stereos and coffeemakers to

gauge the thickness of thin plastics, sheet metal, rubber, textiles and

paper and to measure dust and pollutant levels.

23

Nickel 63: Used to detect explosives and as voltage regulators and

current surge protectors in electronic devices

Phosphorus 32: Used in molecular biology and genetics research.

Sources

International Atomic Energy Agency, In Vienna‘s Art World

Nuclear Science Feeds a “Happy End” Accessed 27 August 2007.

McGraw Hill Dictionary of Scientific and Technical Terms Sci-

Tech Dictionary definition of radioactive tracer (New York,

McGraw – Hill Companies. Inc.2003)

Nuclear Management Company. Medical and industrial uses of

radioactive materials, Accessed 27 August 2007.

Wikipedia Contributors, Radiation therapy, Wikipedia the Free

Encyclopedia. Accessed 27 August 2007.

Wikipedia contributors, Nuclear power, Wikipedia the Free

Encyclopedia Accessed 27 August 2007.

Controlling Exposure to external radiation

Shielding:

There is a variety of shielding materials that can be placed between

you and source to absorb most of the radiation that would otherwise reach

you.

The choice of shielding material depends on the type of radiation

and other functions served by the shields (such as containment,

transparency or structural support).

24

Dense materials with high atomic numbers, such as lead, form the

most effective and compact shields for small sources of penetrating

radiation. Because beta rays are less penetrating than other rays, pure beta

ray emitters can be effectively shielded by lighter materials such as glass,

water or Lucite.

When high ener4gy beta rays are emitted and absorbed secondary

X-ray and bremsstrahlung radiation are generated. The intensity of his

secondary radiation increases if the beta rays are absorbed in high atomic

number shielding material. This secondary radiation is more penetrating

than the beta rays when large quantities (ie. Greater than 100 mCi, or 3.7

GBq) of a pure beta emitter like 32 p are used, the quantity of secondary

radiation may be excessive unless shielded. The best shielding

configuration in this case4 is to use a ½ inch-thick Lucite acrylic sheet or

similar material, adjacent to the 32 p to absorb the beta rays, while

minimizing the creation of secondary radiation. Use sheets of lead foil

outside the shields of Lucite to absorb the more penetrating

bremsstrahlung and x rays.

Fundamental Laws of Radioactivity:

1) Soddy Fajan’s Displacement Law:

When a radioactive disintegration occurs with the emission of

and particles the original atom called the parent atom changes

into same thing else called the daughter. In 1913 Soddy and Fajan

discovered a simple law known as the displacement law of

radioactivity, can be stated as follows.

(a) When a radioactive atom emits and particles (mass 4 and

charge 2e) it is converted into another element of atomic number

25

two less than that of the parent element and the place of the new

atom is shifted two groups lowers in the periodic table.

+

(b) When a radioactive atom emits a particles ( mass approximately

Zero and charge –e) it is converted into another element of atomic

number one greater than that of the parent element but of the same

atomic weight and the place of the new atom is shifted one group

higher in the periodic table.

-1eo

Now a day these rules are stated as follows

a) Algebraic sum of the electric changes before disintegration must be

equal to the total charge disintegration.

b) The sum of mass numbers of the initial particles must be equal to

the sum of mass numbers of the final particles.

2) Law of radioactive disintegration

This law was established expectably in 1902 by Rutherford and

Soddy in Great Britain. They found that the rate at which a particular

radioactive material disintegrates or decays was independent of

physical and chemical condition and was dependent of physical and

chemical condition and was dependent of number of atom present at

that time. Since disintegration is taking place continuously the number

of atoms present is changing hence the rate of disintegration will

change with time.

Let N be the number of atoms present in a particular radio element

at a given instant t. The number of dN that will decay during the time

26

interval dt (from t to t +dt) must be proportional to N and also

proportional to dt.

Thus we have

dN N dt

Or

dN = -l Ndt

Where is constant is known as disintegration constant of the

radioactive element. Negative sign indicates that number of atom of the

radioactive element decreases with time.

On rearranging and integrating equation (1)

We get,

N= No ------------ (2)

Where No is the initial number of atom of the radioactive nuclide.

Here we have assumed that the probability of disintegration per second

is independent of the age of that atom and is the same for all atoms of the

species. For a nuclide having several modes of decay is the probability

of decay and is sum of the probabilities 1, 2 of the individual modes

of decay.

3) Law of Successive Transformation:

In general one radioactive substance decays into another that is

also radioactive. The first is called the parent (or mother) substance, the

second the daughter substance. This relation is not limited to parent and

27

daughter but extends over many generations, until a stable and product is

reached. It was found experimentally that the naturally occurring

radioactive nuclides from three series. In the study of radioactive series it

is important to know the number of atoms of each member of the series as

a function of time.

If a time t = 0 we have N1 (0), N2 (0) …atoms of radioactive

substance 1, 2 …etc.

Respectively Now we have to find the number of atoms N1 (t) N2

(t) …. Present at any subsequent time‘t’

Substance first decays according to the law given by equation (1)

dN1/dt = - N1 1 …………………… (8)

The number of atoms of substance 2 decreases because substance 2

decays and increases because of the decay of substance.

dN2/dt = N1 – N2

From equation (8) the number of atoms N1 can be written as,

N1 = N1(0) ……..(10)

Inserting this value of n1 in equation (9)

We have,

dN2/dt = N1 (0) - N2

Or

dN2/dt + N2 = N1 (0)

28

Multiplying it throughout by and then integrating we have,

N2 = / N1 (0)

Where is a constant of integration

Since N2 = N2 (0) when t = 0 hence we have.

C- N2 (0) - / N1 (0)

N2= / N1 (0)

= / N1 (0) (N2 (0) –N1 / ------------ (11)

This treatment can be extended to a chain of any number of radioactive

products. The procedure is similar to that of the special case already

discussed except that the mathematics becomes more tedious as the

length of the chain increase. The differential equations representing the

number of atoms each member of the series are given as

dN1 /dt = N1

dn2/dt = N1- N2……………………..(12)

- - -

- - -

- - -

dNn /dt = n-1 – n Nn……(13)

The family of differential can be solved by Putting.

N1 = C11 e ………………(14)

29

--- --- ---

--- --- ---

--- --- ---

N2=C2 e +Cn2e +Cnn ------------- (16)

The constants C11, C21, C22 ….Cnn were determined by Bateman under the

assumption that at t = only the parent.

l.e. at t = 0, N1 = N1 (0), N2= N3= N4 = ….=0

from equation (14) we get C11= N1 =(0)

N1= N1 (0)

From equation (12) and (15) we get

0 = C11 e0 + C22 e0 or C21 = -C21

And

C11 = -C22 = N1 (0) – ( C21=- C21)

And

C21 = and

C22 =

N2 = N1 (0)

The number of atoms of the nth member of the chain is obtained by

equation (16) where constants are having values.

30

Cn1=

Cn2=

= exp - 0.766

Table (1-1): Radioactive decay series

Series First Isotopes Half-Life [Y] Last IsotopesUranium 238U 4.49x109 206Pb

Actinium 235U 7.10x108 207Pb

Thorium 232Th 1.39x1010 208Pb

Neptunium 237Np 2.17x106 209Bi

There are three natural radioactive series, called uranium, thorium

and actinium series. Neptunium series is included in this table too, which

does not occur in nature because it’s half life “2.1x106 y” is much smaller

than the age of the universe “3x109 y” [46].

1.2. a: U-238 Series

This series begins with U-238 nuclei (half-life 4.49x109y) and

gradually converted to the Pb-206 which is a stable element through

sequences of the emission of alpha and beta particles. All nuclides in this

31

series are solid elements except Rn-222 nuclei, which is gas. The

elements of this series which are represented in Table (1-2) are arranged

according to the mass number indicated in (4n+2) system.

Table (1-2): U-238 Decay Series [47, 78]

1.2. b: U-235 Series

This series begins with U-235 nuclei (half life 7.10x108 y), which

is the longest half life comparing to other elements in this series and ends

with Pb-207, which is a stable element. The elements of this series which

are represented in Table (1-3) are arranged according to the mass number

indicated in (4n+3) system.

Nuclide Half-life Type of decay

U-238 4.49x109y Alpha

Th-23 24.1 d Beta

Pa-234m 1.18 min Beta

U-234 2.48x105 y Alpha

Th-230 7.52x104 y Alpha

Ra-226 1600 y Alpha

Rn-222 3.825 d Alpha

Po-218 3.05 min Alpha

Pb-214 26.8 min Beta,

Bi-214 19.7 min Beta

Po-214 1.6x10-4s Alpha

Pb-210 22 y Beta

Bi-210 5.01 d Beta

Po-210 138.4 d Alpha

Pb-206

32

Table (1-2): U-238 Decay Series [47, 78]

1.2. c : Th-232 Series

Thorium was discovered by “Berzelius”, which is derived from the

Scandinavian god “Thor”. This series begin with Th-232 nuclei (half life

1.39x1010 y) and end with Pb-208 isotope. The elements of this series

which are represented in Table (1-4) are arranged according to the mass

number indicated in (4n) system.

Table (1-4): Th-232 Decay Series [47-48]

Nuclide Half-life Type of decay

Nuclide Half-life Type of decay

U-235 7.10x108 y Alpha

Th-231 25.6 h Beta

Pa-231 3.98x104 y Alpha

Ac-227 22 y Beta

Th 227 or Fr-233

18.17 d

22 min

Alpha

Beta

Ra-223 11.7 d Alpha

Rn-219 3.92 s Alpha

Po-215 1.83x10-3 s Alpha

Pb-211 36.1 min Beta,

Bi-211 2.15 min Alpha

Po-211 0.52 sec Alpha

Ti-207 4.79 min Beta

Pb-207 Stable ---

33

Th-232 1.39x1010 y Alpha

Ra-228 6.7 y Beta

Ac-228 6.13 h Beta

Th-228 1.9 y Alpha

Ra-224 3.64 d Alpha

Rn-220 54.5 s Alpha

Po-216 0.158 s Alpha

Pb-212 10.6 h Beta

Bi-212 60.0 min Beta

Ti-208or

Po-212

3.1 min

3.0x10-7 s

Beta

Alpha

1.2. d: Np-237 Series

Np-237 which a half-life (2.14x106 y), which is much shorter than

the geological age of the earth. Virtually all neptunium decayed within

the first 50 millions of years after the earth was formed [45]. So 237Np

did not find in nature but it discovered in some` stars spectrum [49].

CHAPTER - II

34

INTRODUCTION TO BIOMOLECULE

Biomolecules:

A biomolecule is defined as an organic compound which is found

in almost all the living organisms. These are the molecules that are

composed of carbon, hydrogen, oxygen, nitrogen, sulfur, phosphorus and

sometimes some other elements to a very small extent.

Importance of Biomolecule:

Biomolecule play a very important role in the functioning of living

organization and therefore these are considered as the building blocks of

life.

Biomolecule are essential for life to exist. These molecules make

up and control a living organism’s body. These play a vital role in the

development of living organization. An organism needs each and every

biomolecule in a proper amount for the functioning and well being of his

body. Each biomolecule has a certain task and duty that keeps the body

healthy and control it.

Biomolecule are necessary for the existence of all known forms of

life. For example, humans possess skin and hair. The main component of

hair is keratin, an agglomeration of proteins which are themselves

polymers built from amino acids. Amino acids are some of the most

important building blacks used, in nature, to construct larger molecules.

Another type of building block is the nucleotides, each of which consists

of three components; a Purina or pyramiding base, a pentose sugar or a

phosphate group these nucleotides, mainly, from the nucleic acids.

35

Beside the polymeric biomolecule, numerous small organic

molecules are absorbed or synthesized by living systems. Many

biomolecule may be useful or important drugs.

Type of Biomolecule:

Biomolecule ranges from a small molecule to large polymers.

A. Small Molecules mainly include molecules like :

Lipids such as phospholipids, glycolipids, sterols, and

glyceroliopids: - are the main components or biological membranes

and as function as the highest energy providing molecules.

Carbohydrates such as sugars also provide energy and act as

energy storage molecules.

Vitamins though not synthesized by organisms, are important

biomolecule, which are necessary for the survival and health of

organization.

Hormones, neurotransmitters and metabolites: hormones regulate

the metabolic processes and many other functions of organisms.

B. Monomers include :

Amino acids: buildings blocks of proteins function as genetic code

and as biomolecule that assist in other processes such as lipid

transport.

Nucleotides: They are the source of chemical energy (ATP, GTP),

assist in cellular signaling, and participate in important enzymatic

reaction (coenzyme A, flavin) adenine dinucleotide, flavin

mononucleotide, nicotinamide adenine dinucleotide phosphate etc.)

36

Monosaccharide: Provides energy and are the building blocks of

polysaccharides.

C. Polymers include following organic compounds :

Peptides ologopeptides, polypeptides or proteins: Play multiple

functions in an organism’s body. They work as enzymatic

catalysts, transport molecules (hemoglobin transports oxygen) and

storage molecules. These are the major components of muscles;

they are needed for mechanical support. These biomolecule

mediate cell responses. Antibody proteins are the main part

immune system. Hormonal proteins control growth and cell

differentiation. Many such other functions are performed by these

biomolecule.

Nucleic acids, DNA, RNA: are the biomolecule that are involved

in heredity.

Oligosaccharides, polysaccharides cellulose, lignin: Structural

molecules and provide energy.

Biomolecule - Amino - Acids:

Amino acids are molecules that contain both amino and carboxylic

acid functional groups. (In biochemistry, the term amino acid is used

when referring to those amino acids in which the amino and carboxyl ate

functionalities are attached to the same carbon plus praline which is not

actually an amino acid.) Amino acids are the building blocks of long

polymer chains. With 2-10 amino acids such chains are called peptides,

with 10-100 they are often called polypeptides, and longer chains are

known as proteins. These protein structures have many structural and

functional roles in organisms. There are twenty amino acids that are

encoded by the standard genetic code, but there are more than 500 natural

37

amino acids. When amino aids other than the set of twenty are observed

in proteins, this is usually the result of modification after translation

(protein synthesis). Only two amino acids other than the standard twenty

are known to be incorporated into proteins during translation, in certain

organization.

Selenocysteine is incorporated into some proteins at a UGA

cordon, which is normally a stop cordon.

Pyrrolysine is incorporated into some proteins at a UAG cordon.

For instance, in some methanogens in enzymes that is used to produce

methods.

Beside those used in protein synthesis, other biologically important

amino acids include carnitine (used in lipid transport within a cell),

ornithine, GABA and taurine.

Amino Acids:

Amino acids are organic compounds, containing an amino group

and a carboxyl group. Amino acids are the end product of protein

digestion and the basic building blocks from which proteins are

synthesized in the cell.

Amino acids are the chemical units that make up proteins, as they

are famously called the “building blocks” of protein.

Amino acids combine with nitrogen and form thousands of

different proteins. However, they are not only the chemical units from

which proteins are formed, but are also the end products of protein

digestion.

38

Proteins provide structure for all living things, from the largest

animal to the tiniest microbe and, as such, ion its various forms, protein

participates in the vital chemical processes that sustain life.

In the human body, proteins are a necessary part of every living

cell and next to water; proteins make up the greatest portion of our body

weight. The body breaks these proteins down into their constituent parts,

and then our cells use these to build the specific types of protein each of

them needs.

There are twenty-eight commonly known amino acids. Nine of

these are called essential amino acid. They are; instideine, isoleucine,

leucine, lysine, methionine, phenylalanine, threonine, tryptophan, and

valine. These nine essential amino acids cannot be manufactured by the

body and must be obtained from food or supplements.

The remaining nineteen are referred to as non-essential amino

acids, meaning they can be manufactured by the body from other amino

acids as needed, but they too can be obtained through supplements. The

term “nonessential” amino acids does not mean they are not necessary

and they provide no amino acid benefits, only that they need not be

obtained through diet because the body can manufacture them as needed.

However, a nonessential amino acid can become “essential” under

certain situations. For example, the nonessential amino acids cysteine and

tyrosine are derived from the essential amino acids methionine and

phenylalanine. If these two essential amino acids are not available in

sufficient quantities, cysteine and tyrosine than become essential in the

diet.

39

Amino acid - General Structure:

There are basically 20 standard amino acids having different

structures in their side chains (R group). The common amino acids are

known as a-amino acids because they have a primary amino group (-

NH2) and a carboxylic acid group (-COOH) as substitutes of the carbon

atoms. Proline is an exception because it has a secondary amino group (-

NH-), for uniformity it is also treated as alpha-amino acid.

Fig 1 general structure of a-amino acid.

Where “R” represents a side chain specific to each amino acid.

Amino acids are usually classified by properties of the side chain into

four groups: acidic, basic, and hydrophilic (polar), and hydrophobic

(nonpolar).

Functional Significance of Amino Acid R-Groups:

In solution it is the nature of the amino acid R-groups that dictate

structure-function relationship of peptides and proteins. The hydrophobic

amino acids will generally be encountered in the interior of proteins

shielded from direct contract with water. Conversely, the hydrophilic

amino acids are generally found on the exterior of proteins as well as in

the active centers of enzymatically active proteins. Indeed, it is the very

nature of certain amino acid R-groups that allow enzyme reactions to

occur.

40

R

H2N C COOH

H

The imidazole ring of histidine allows it to act as either a proton

donor or acceptor at physiological pH. Hence, it is frequently found in the

reactive center of enzymes. Equally important is the ability of histidines

in hemoglobin to buffer the H+ ions from carbonic acid ionization in red

blood cells. It is property of hemoglobin that allows it to exchange O2 and

CO2 at the tissues or lungs, respectively.

The primary alcohol of serine and threonine as well as the thiol (-

SH) of cysteine allow these amino acids to act as nucleophiles during

enzymatic catalysis. Additionally, the thiol of cysteine is able to form a

disulfide bond with other cysteines.

General Properties:

The amino and carboxylic acid groups of amino acids readily

ionize. At a pH (~7.4), the amino groups are protonated and the carboxyl

acid groups are in their conjugate base (carboxylate) form, this shows that

an amino acid that can act as an Acid and also a base. Amino acids can

bear charged groups of opposite polarity, hence they are known as

zwitterions or dipolar ions. The ionic property of the side chains

influences the physical and chemical property of free amino acids and

amino acids in proteins.

Peptide Bonds:

Elimination of water (condensation) can polarize amino to form

long chains. The resulting CO-NH linkage, an amide linkage, is known as

peptide bond. Polymers composed of two, three, a few (3-10), and many

amino acid units are known, respectively, as dipeptides, tripeptides,

oligopeptides, and polypeptides, commonly they are called “peptides.”

Peptide bond formation is a condensation reaction leading to the

polymerization of amino acids into peptides and proteins. Peptides are

41

small consisting of few amino acids. A number of hormones and

neurotransmitters are peptides. Additionally, several antibiotics and

antitumor agents are peptides. Proteins are polypeptides of greatly

divergent length. The simplest peptide, a dipeptide, contains a single

peptide bond formed by the condensation of the carboxyl group of one

amino acid with the amino group of the second with the concomitant

elimination of water. The presence of the carbonyl group in a peptide

bond allows electron resonance stabilization to occur such that the

peptide bond exhibits rigidity not unlike the typical -C=C- double bond.

The peptide bond is, therefore, said to have partial double-bond character.

Classification:

There are basically three manor classifications for amino acid (1)

those with nonpolar R group, (2) those with uncharged polar R groups,

and (3) those with charged polar R group. The table below shows us all

20 amino acids with their codes.

Table 1:20 Standard amino acids

Sr. No.

One-letter code

Three-letter code Name

1 A Ala Alanine

2 C Cys Cysteine

3 D Asp Aspartic Acid

42

O O

C C

NH NH+

4 E Glu Glutamic Acid

5 F Phe Penylalanine

6 G Gly Glycine

7 H His Histidine

8 I Ile Isoleucine

9 K Lys Lysine

10 L Leu Leucine

11 M Met Methionine

12 N Asn Asparagines

13 P Pro Proline

14 Q Gln Glutamine

15 R Arg Arginine

16 S Ser Serine

17 T Thr Threonine

18 V Val Valine

19 W Trp Tryptophan

20 Y Tyr Tyrosine

Non-polar amino acids side chains have a variety of shapes and

sizes; there are basically nine acids under this classification. Glycine has

the smallest possible side chain, an H atom. Alanine, valine, leucine, and

isoleucine have aliphatic hydrocarbon side chains ranging in size from a

methyl group for alanine to isomeric butyl groups for leucine and

isoleucine. Methionine has a thiol ether side chain that resembles an n-

butly group is man of its physical properties (C and A have nearly equal

electronegativities, and S is about the size of a methylene group). Proline

has a cyclinc pyrrolidien side group. Phenylalanine (with its phenyl

43

moiety) and typtophan (with its indole group) contain aromatic side

groups, which are characterized by bulk as well as nonoplarity.

Uncharged Polar side chains have Hydroxyl, Amide, or Thiol

Groups. There are six amino acids under this. Serine and threonine have

hydroxylic R side chains of different sizes. Tyrosine has a phenolic group

and is aromatic. Cystein is very unique among all 20 amino acid because

it has a thiol group that forms a disulfide bond with other Cystein through

oxidation.

Charged Polar side chains, they are positivity or negatively

charged. Five amino acids contribution to this types. The side chains are

positively charged; they are lysine, which has a butylammonium side

chain, arginine, which has a guanidine group, and histidine, which bears

imidazolium moiety.

Physical Properties:

Melting Points:

The amino acids re-crystalline solids with surprisingly high

melting points. It is difficult to pin the melting points down exactly

because the amino acids tend to decompose before they melt.

Decomposition and melting tend to be it the 200-3000C range.

For the size of the structure of an amino acid, you will see that it

has both amine group and an acidic carboxylic acid group.

basic group

NH2

R-CH-COOH

acidic group

44

There is an internal transfer of a hydrogen ion from the -COOH

group to the- NH2 group to leave in ion with both a negative charge and

positive charge. This is called zwitterions.

NH3+

R-CH-COO-

a zwitterions

Zwitterions are a compound with no overall electrical charge, but

which contains separate parts which are positively and negatively

charged.

This is the form that amino acids exist in even in the solid state.

Instead of the weaker hydrogen bonds and other intermiluecular forces

that you might have expected, you actually have much stronger ionic

attractions between one ion and its neighbors.

These ionic attractions take more energy to break and so the amino

acids have high melting points for the size of the molecules.

Solubility:

Amino acids are generally soluble in water and insoluble in non-

polar organic solvents such as hydrocarbons.

This again reflects the presence of the zwitterions. In water, the

ionic attractions between the ions in the solid amino acid are replaced by

strong attractions between polar water molecules and the zwitterions.

This is much the same as any other ionic substance dissolving in water.

The extent of the solubility in water varies depending on the size and

nature of the “R” group.

45

The lack of solubility in non-polar organic solvents such as

hydrocarbons is because of the lack of attraction between the solvent

molecules and the zwitterions. Without strong attractions between solvent

and amino acid, there won’t be enough energy released to pull the ionic

lattice apart.

Optical Activity:

If you look yet again at the general formula for an amino acid, you

will see that (apart from glycine, 2-aminoethanoci acid) the carbon at the

centre of the structure has four different groups attached. In glycine, the

“R” group is another hydrogen atom.

NH3+

R-CH-COO-

four different groups attached to this carbon atom

This is equally true if you draw the structure of the zwitterions

instead of this simpler structure.

Because of these four different groups attached to the same carbon

atom, amino acids (apart from glycine) are chiral.

The lack of a plane of symmetry means that there will be two

stereoisomers of an amino acid (apart from glycine) - one the non-

superimposable mirror image of the other.

46

For a general 2-amino acid, the isomers are:

II H

C C

R COOH COOH R

NH2 HN2

mirror

Optical Properties of the Amino Acids:

A tetrahedral carbon atom with 4 distinct constituents is aid to be

chiral. The one amino acid not exhibiting chirality is glycine since its “R-

group” is a hydrogen atom. Chirality describes the handedness of a

molecule that is observable by the ability of a molecule to rotate the plane

of polarized light either to the right (dextrorotatory) or to the left

(levorotatory). All of the amino acids in proteins exhibit the same

absolute steric configuration as L-glyceraldehyde. Therefore, they are all

L-α-amino acids. D-amino acids are never found in proteins, although

they exist in nature. D-amino acids are often found in polypeptide

antibiotics.

The aromatic R-groups are amino acids absorb ultraviolet light

with an absorbance maximum in the range of 280nm. The ability of

proteins to absorb ultraviolet light is predominantly due to the presence of

the tryptophan which strongly absorbs ultraviolet light.

Chemical Nature of the Amino Acids:

All peptides and polypeptides are polymers of α-amino acids.

There are 20 α-amino acids that are relevant to the make-up of

mammalian protein (see below). Several other amino acids are found in

47

the body fee or in combined state (i.e. not associated with peptides or

proteins). These non-protein associated amino acids perform specialized

functions. Several of the amino acids found in proteins also serve

functions distinct from the formation of peptides and proteins, e.g.,

tyrosine in the formation of thyroid hormones or glutamate acting as a

neurotransmitter.

The α-amino acid in peptides and proteins (excluding proline)

consist of a carboxylic acid (-COOH) and an amino (-NH2) functional

group attached to the same tetrahederal carbon atom. This carbon is the α-

carbon. Distinct R-groups, that distinguish one amino acid from another,

also are attached to the alpha-carbon (except in the case of glycine where

the R-group is hydrogen). The fourth substitution on the tetrahedral α-

carbon of amino acids is hydrogen.

Table of α-Amino Acids Found in Proteins:

Amino Acid Symbol Structure pK1

(COOH)pK2

(NH2)pK R

Group

Amino Acids with Aliphatic R-Groups

Glycine Gly-GH-CH-COOH

NH2

2.4 9.8 -

Alanine Ala-ACH3-CH-COOH

NH2

2.4 9.9 -

Valine Val-V CH-CH-COOH

NH2

2.2 9.7

Leucine Leu-L CH2-CH-COOH

NH2

2.3 9.7

48

H3C

H3C

H3C

H3C

Isoleucine Ile-I CH-CH-COOH

NH2

2.3 9.8

Series Ser-S HO-CH2-CH-COOH

NH2

2.2 9.2 ≈13

Threonine Thr-S CH-CH-COOH

NH2

2.1 9.1 ≈13

Amino Acids with Sulfur-Containing R-Groups

Cysteine Cys-C HS-CH2-CH-COOH

NH2

1.9 10.8 8.3

Methionine Met-MH3S-S-(CH2)2-CH-COOH

NH2

2.1 93 -

Acidic Amino Acids and their Amides

Aspartic Acdi Asp-D

HOOC-CH2-CH-COOH

NH2

2.0 9.9 3.9

Asparagine Asn-NH2N-C-CH2-CH-COOH

O NH2

2.1 8.8

Gultamic Acid Asn-N

HOOC-CH2CH2-CH-COOH

NH2

2.1 9.5 4.1

Gultamine Gln-QH2N-C-CH2-CH2-CH-COOH

O NH2

2.2 9.1

Basic Amino Acids

Arginine Arg-R

HN-HC2-CH2CH2-CH-COOH

C=NH NH2

NH2

1.8 9.0 12.5

Lysine Lys-K H2N-(CH2)4-CH-COOH 2.2 9.2 10.8

49

H3C-H2C

H3C

H3C

HO

NH2

Histidine His-HCH2-CH-COOH

NH2

1.8 9.2 6.0

Amino Acids with Aromatic Rings

Phenylalnine Phe-F CH2-CH-COOH

NH2

2.2 9.2

Tyrosine Tyr-Y HO CH2-CH-COOH

NH2

Tryptophan Trp-WCH2-CH-COOH

NH2

Amino Acids

Proline Pro-PCOOH

2.0 10.6

Acid-Base Properties of the Amino Acids:

The α-COOH and α-NH2 groups in amino acids are capable of

ionizing (as are the acidic and basic R-groups of the amino acids). As a

result of their ionizability the following ionic equilibrium reactions may

be written:

R-COOH R-COO-+H+

R-NH3+ R=NH2+H+

The equilibrium reactions, as written, demonstrate that amino acids

contain at least two weakly acidic groups. However, the carboxyl groups

is a far stronger acid than the amino group at physiological pH (around

7.4) the carboxyl group will be unprotonated and the amino group will be

50

protonated. An amino acid with no ionizable R-group would be

electrically neutral at this pH. This species is termed zwitterions.

Like typical organic acids, the acidic strength of the carboxyl,

amino and ionizable R-group in amino acids can be defined by the

association constant, Ka or more commonly the negative logarithm of Ka,

the pKa. The net charge (the algebraic sum of all the charged groups

present) of any amino acid, peptide or protein, will depend upon the pH

of the surrounding aqueous environment. As the pH of a solution of an

amino acid or protein changes so too does the net charge. This

phenomenon can be observed during the titration of any amino acid or

protein. When the net charge of an amino acid or protein is zero the pH

will be equivalent to the isoelectric point: ph.

Amino Acid Benefits:

Amino acids are vital to vibrant health. Put simply, amino acids are

utilized to make crucial substance within the body.

51

For example, they are utilized to make enzymes that support

biochemical reactions, and hormones that influence body’s metabolism.

They are also utilized to make hemoglobin that carries oxygen through

the body, and antibodies that are infection fighters that help the immune

system.

Amino acids even have a role in repairing muscles, ligament,

tendons organ, glands, nails, and hair.

Moreover, some amino acids act as neurotransmitters, chemicals

that play a crucial role in transmitting messages within the neurons of the

brain, while others are involved in detoxification reactions and metabolic

function.

Amino acids also enable vitamins and minerals to carry out their

jobs properly and efficiently.

In other words, the lists of amino acid benefits are long because

they are crucial to vibrant health and, as such, deficiencies in just one of

them severely compromise your health.

Amino acids and their functions in the body:

ARGININE :

o Studies have shown that it has improved immune response to

bacteria, viruses and tumor cells. Arginine promotes healing and

regeneration of the liver. It also causes the release of growth

hormones; considered crucial for optimal muscle growth and tissue

repair.

52

L-ARGININE: Important for cardiovascular health and more.

ALANINE :

o This non-essential amino acid-which may be considered essential

under some circumstances, is an important source of energy for

muscle tissue, the brain and central nervous system. It helps in the

metabolism of sugars and organic acids, and may also help

stabilize the blood glucose levels in people with hypoglycemia.

ASPRARTIC ACID :

o Aspartic acid is a non-essential amino acid, aiding in the expulsion

of harmful ammonia from the body. When ammonia enters the

circulatory system, it acts as a highly toxic substance which can be

harmful to the central nervous system. Its ability to increase

endurance is thought to be a result of its role in clearing ammonia

from the system. Athletes use it to promote stamina and endurance.

The popular sweetener Aspartame is a combination of Aspartic

acid and phenylalanine. Aspartic acid is considered nontoxic. Some

research has shown that Aspartic acid might be useful in opiate

withdrawal.

CYSTINE :

o It functions as a powerful antioxidant and an immune support

substance, neutralization free radicals. It can help slow down the

again process. It is necessary for the formation of the skin, and aids

in the recovery from burns and surgical operation.

GLUCOSAMINE :

o Glucosamine consists of glucose combined with the amino acid

Glutamic Acid. Studies have shown that Glucosamine sulfate may

be of use in treating osteoarthritis or degenerative joint disease.

53

This natural provides the body with an important raw material that

appears to halt the disease process. Itself. In the body, the main

action of glucosamine on joints is to stimulate the manufacture of

substance necessary for joint repair.

o Glucosamine has also been shown to exert a protective effect

against joint destruction and, when taken orally, is selectively taken

up by joint tissues to exert a powerful therapeutic effect.

GLUTAMIC ACID :

o This amino acid has been shown to improve mental capacities,

speeds, the healing process of ulcers, and gives a lift from fatigue.

It also helps control alcoholism and the craving for sugar.

GLYCINE :

o These non-essential amino acids is required by the body for the

maintenance of the central nervous system, and in men, glycine

plays an essential role in maintaining healthy prostate functions. It

helps trigger the release of oxygen to the energy requiring cell-

making process as well as providing nutrients to support a strong

immune system and free radical fighters.

ORNITHINE :

o Ornithine is important since it induces the release of growth

hormones in the body, which in turn helps with fat metabolism. It

is further required for a properly functioning liver and immune

system ornithine assists in the ammonia detoxification and

rejuvenation of the liver. It is also useful in healing and reparing

skin and tissue and is found in both these body parts. There are

some unsupported claims that ornithine also promotes muscle

building, but this has not been proven.

54

PROLINE :

o Proline is a non-essential amino acid, which improves skin texture,

and proper functioning of joints and tendons. It also helps maintain

and strengthen heart muscles. Proline is most effective when

adequate Vitamin C is supplied at the same time.

SERINE :

o Serine is a non-essential amino acid that is needed for the

metabolism of fats and fatty acids, for muscle growth, and for a

healthy immune system. There is some concern that elevated serine

levels (especially) in sausage and lunch meats) can cause immune

suppression and psychological such as cerebral allergies.

TYPROSINE :

o Tyrosine is a non-essential amino acid that is used by the thyroid

gland to produce one of the major hormones, Thyroxin. This

hormone regulates growth rate, metabolic rate, skin health and

mental health. It is used in the treatment to control anxiety,

allergies and headaches. Tyrosine is known as the “anti-

depressant” amino acid and serves as the building block for the

hormones dopamine and nor epinephrine which create a sense of

pleasure and well-being. Tyrosine can also act as a mild appetite

suppressant.

TAURINE :

o Taurine is a non-essential amino acid that functions in electrically

active tissues such as the brain and heart, to help stabilize cell

membranes. Supplements decrease the tendency to develop

abnormal heart arrhythmia after heart attacks. People with

55

congestive heart failure have also responded to supplementation

with improved cardiac and respiratory function.

L-CARNITINE :

o In the strictest sense L Carnitine is not an amino acid, but a

substance related to the B vitamins. However, due to its chemical

structure, which is similar to those amazing amino acids it is

usually considered together with them. Learn all about its role in

transporting fatty acids into energy producing units in cells.

56

CHAPTER - III

CROSS SECTION

The concept of the cross section, σ, has been introduced for the

purpose of calculating the attenuation of the incident beam.

Consider a beam of particles of intensity I incident on a thin sheet

of material of thickness dt and café area A. as a particles passes through

the thin sheet there is some chance that it will be absorbed by a nucleus, if

the particle happens to come close to it. Assume that σ is the effective

area surrounding an atom, such that if the incident particle falls within

this area (fig. 1), the nuclear reaction will take place. Let there be n target

nuclei per unit volume of the sheet. It is assumed that the foil is so thin

that none of the nuclei overlap each other so as to be equally probable to

cause the nuclear reaction with the incident particles. With this notation

in mind, we have

n dt = number if nuclei per unit face area,

A n dt = total number of nuclei in the face area A

Fig. 1: a beam of particles incident on a thin foil.

Because with each nucleus is associated an effective area, σ, the

total sensitive area or effective area available for a nuclear reaction is,

A n σ dt = total effective area

57

The fractional effective, f, is given by’

f = total effective area = σ A n dt / A = nσ dt (1)

total face area

This fraction effective area represents the fractional change in the

intensity of the beam as passes through the foil. Thus the change in the

intensity is given by

dI = -fI (2)

Note that because we are talking in terms of probabilities, f and,

consequently σ have nothing to do with the geometrical size of the atom.

Actually proportional to the probability for a nuclear reaction to take

place. Combining Eqs. (1) and (2) we get

-dI/I= n σdt (3)

Where the negative sign means the intensity I decrease as thickness

increases. Assuming I=I0 at t=0 and integrating Eq. (3) we get

I=I0e-nσ (4)

Because the number of particles N in the beam is proportional to

the intensity of the beam, Eq. (4) in terms of the number of particles, can

be written as

N=N0e-nσt (5)

Where N0 is the number of particles incident on the foil, and N is

the number of particles left after traversing a thickness t of the foil.

The microscopic-cross-section or simply the cross section is

usually denoted by σ. The unit of the cross section is the barn, or b, where

1b=10-24 cm2

58

And a smaller unit is the mill barn, denoted by mb

1 mb=10-3 b

The product of n and σ is called the macroscopic cross section Σ

Σ = nσ (6)

If we are dealing with absorption only, then sometimes the term

absorption coefficient, α is used instead of Σ, where

Α = nσ (7)

Eq. (5) can be written as

N=N0e-Σt = N0e-αt (8)

The meaning of a thin foil can now made clear. The foil is said to

be thin if αt<< 1, which is true either if the foil is sufficiently

geometrically thin or if the cross section is sufficiently small in this case.

e-αt = 1 - αt

N=N0 (1-αt)

Thus the number of particles absorbed while traversing a thickness t, is

given by

dN = N0-N0 (1-αt) = N0α t = N0n αt (9)

Note that this is in complete agreement with the definition of

fractional effective area (f=nσ dt)

Gamma Radiation:

Gamma radiation, also known as gamma rays (denoted as γ), is

electromagnetic radiation of high frequency (very short wavelength).

They are produced by sub-atomic particles interactions such as electron-

positron annihilation, neutral pion decay, radioactive decay (including

isomeric transition which involves an inhibited gamma decay), fusion,

fission or inverse Compton scattering in astrophysical processes. Gamma

59

rays have frequencies above 10 (1019 Hz), and therefore have energies

above 100 keV and wavelength less than 10 picometers, often smaller

than an atom. Gamma rays from radioactive decay commonly have

energies of a few hundred keV, and almost always less than 10 MeV. The

highest energy detected as of September 2009 is 33 GeV, and there is

effectively no lower limit (they are sometimes classed as X-rays if their

frequencies are lower than 1019 Hz). Because gamma rays are a form of

ionizing radiation, they pose a health hazard.

Paul, Villard, a French chemist and physicist, discovered,

discovered gamma radiation in 1900, while studying radiation emitted

from radium. Alpha and beta “rays” had already been separated and

named by the work of Ernest Rutherford in 1899, and in 1903 Rutherford

named Villard’s distinct new radiation “gamma rays.”

The distinction between X-rays and gamma rays has changed in

recent decades. Originally, the electromagnetic radiation emitted by X-

rays tubes had a londer wavelength than the radiation emitted by

radioactive nuclei (gamma rays). Older literature distinguished between

X-and gamma radiation on the basis of wavelength, with radiation shorter

than some arbitrary wavelength, such as 10-11 m, defied as gamma rays.

However, as shorter wavelength continuous spectrum “X-ray” source

such as linear accelerators and longer wavelength “gamma ray” emitters

were discovered the wavelength bands largely overlapped. The two types

of radiation are now usually distinguished by their origin: X-rays are

emitted by electrons outside the nucleus, while gamma rays are emitted

by the nucleus.

60

Absorption coefficient of Gamma ray photons:

The intensity of a beam of γ- rays passing through a material

followed the exponential law of absorption, because the change in

intensity is directly proportional to the incident intensity and the

thickness of the material. Let us consider a beam of photons with

intensity I falling perpendicular to material of thickness ∆x. then the

change in intensity, ∆I, is given by

∆I= - µI∆x (1)

Where µ is the proportionality constant and is known as the absorption

coefficient.

For a given material, µ is different for photons of different

energies. The negative sing in Eq. (1) indicates that the intensity

decreases with increasing thickness. Thus for a homogeneous radiation, :

is constant and from Eq. (1) we get

I=I0e-µx (2)

Where I is the intensity of the beam after the beam of initial

intensity, I0, has crossed a thickness x of the material.

Due to the exponential nature of their absorption, gamma rays do

not have a definite range as do alpha and beta particles but are

characterized by the attenuation absorption coefficient, µ. Also we may

write

I=hvΦ (3)

Where hv is the energy of each photon, Φ is the number of photons

crossing a unit area in a unit time and is called the flux. Combining Eqs.

(2) and (3), we get

Φ=Φ0e-µx (4)

61

Where Φ is the initial flux. Note that I denotes the energy flux (or

intensity), and Φ is the number of flux, µ is sometimes called as the liner

absorption coefficient.

Besides the liner absorption coefficient, µ, the other coefficient that

are commonly used are mass absorption coefficient, µm, atomic

absorption coefficient eµ and electronic absorption coefficient eµ. These

four coefficients are related to each other in the following way:

aµ = Z eµ

µ = (ρ NA/A) aµ = (ρ NAZ/A) eµ

µm = (µ/ρ) = (NA aµ/A) eµ

Where Z is the atomic number, A is the atomic weight, ρ is density

in g/cm3, and NA is the Avogadro’s umber. Because µx is a dimensionless

quantity, x is expressed in cm, µ will be in cm-1. Accordingly, for the

mass absorption coefficient, µm, x is expressed in gm/cm2 and µm in

cm2/gm. Similarly if x is expressed in atoms/cm2 or electron/cm2, aµ and

eµ are expressed as cm2/atom and cm2/electron, respectively.

Because Z/A changes very slowly with increasing Z, and eµ is the

same for all elements in a certain energy range, this leads to the

conclusion that µm does not vary much for all elements in this energy

range.

The half-thickness, x1/2 is characteristics of the absorber as the half

life of the decaying nucleus, x1/2 is defined as thickness that reduces the

incident beam intensity to one-half of its initial intensity, i.e.,

I/I0=1/2=e-µx1/2

or

x1/2=0.693/µ=0.693/ρµm (6)

62

If the incident beam consists of photons of different energies, Eq.

(4) is replaced by the following equation

Φ=Φ01e-µ1x+Φ02e-µ2x+Φ03e-µ3x+…… (7)

Where Φ01, Φ02, Φ03, and µ1, µ2, µ3 … are the initial fluxes and

absorption coefficient, respectively, of photons with energies hv1, hv2,

hv3…

Coefficient, µ, used above is actually the sum of two processes:

i) The process in which the photon loses its energy in whole or in part to

a particle, which in turn easily absorbed. The energy, therefore, is

deposited inside the material, and

ii) The process in which photons are scattered outside the beam with no

absorption of energy in the martial. We many write µ, therefore, as the

sum of two terms,

µ=µa+µs (8)

Where µa corresponds to absorption and µs to scattering.

Interaction of gamma ray photon with matter:

There are numerous processes by which gamma rays interact with

the matter and lose their energy. Fortunately, all these process do not

contribute to the same extent for different energy photons. The gamma

rays emitted in the nuclear decay usually have energies ranging from a

fraction of a Mev to a few Mev. In this range, the three main processes by

which photons lose their energies by interaction with matter are:

a) Photoelectric effect (P.E.)

b) Compton effect (C.E.)

c) Pair production (P.P.)

63

These are not the only processes that gamma rays interact with

matter. The other processes by which gamma rays interact with matter

are, although they do not contribute much to the absorption coefficient

that is in low energy of gamma rays.

They are as follows:

Rayleigh scattering : This is the famous classical coherent-scattering

(elastic scattering), and it takes place whenever the incident photons

fall on bound electrons, provided the electrons do not get enough

energy to the ejected from the atom. Thus, it will be more prominent

at low photon energies and absorbs with high Z.

Thomson scattering: This may also be called Nuclear Compton-

scattering and takes places between the incident photon and a nucleus

instead of a free electron. Because of the large mass of the nucleus, the

effect is very small.

Nuclear photoelectric effect: In this process the high-energy photon

may be absorbed by the nucleus, resulting in the ejection of a nucleon.

This is the so called photodisintegration, and it is more prevalent for

high Z.

Nuclear-resonance scattering: In this process the nucleus is excited by

the absorption of incident photon haven energy equal to the difference

between two nuclear energy levels. This is followed by the de-

excitation of the nucleus.

Elastic nuclear-scattering (or Delbruck scattering): The scattering of a

photon may be caused by the electromagnetic field of the nucleus.

The three process i.e. Photoelectric (P.E.), Compton Effect (E.E.), Pair

Production (P.P.) are dominant in different range of the photon energy.

64

The photoelectric effect from ~ 0.01 Mev to ~0.5 Mev, the Compton

scattering from ~0.1 Mev to ~10 Mev, and Pair production start at 1.02

Mev and increase with increasing gamma energy. All three are

independent of each other and by analogy with

∆I=µI∆x (a)

We may write,

(∆I)P.E. =-µτI∆x (1)

(∆I)C.E. = -µσI∆x (2)

(∆I)P.P. = -µkI∆x (3)

Where µι µσ and µk are absorption coefficients for the photoelectric

effect, the Compton Effect, and pair production, respectively. Adding all

three together, we may write.

∆I= +(∆I)P.P. + (∆I)C.E. + (∆I)P.E.

= - (∆τ+µσ+µk) I∆x (4)

and comparing with Eq. (a), we get

µ=µτ+µσ+µk (5)

(a) Photoelectric effect (P.E.): (predominates in the energy range 0.1 Mev

to 5 Mev). This effect is more prominent at low energies of the incident

photon. The incident photon is absorbed by one the electrons of the atom.

In the process the photon disappears and electron in ejected (Fig. 1),

kinetic energy Ke, is given by

Ke=hv-IB (6)

65

Where hv is the energy of the incident photon, and IB is the binding

energy of the orbital electron. It is impossible for a free electron to absorb

a photon because it will not converse both momentum and energy. But in

the case of a bound electron, the atom recoils and therefore, conserves the

momentum. Because the mass of the atom is very large, its recoil energy

is small, and it has been neglected in Eq. (6)

Fig. 1 The photoelectric effect; absorption of a photon results in the

emission of K-electron

The theoretical calculations for the cross section of the

photoelectric effect involve the use of Dirac’s relativistic equation for a

bound electron. This makes evaluation difficult. For different regions of

energy of the photons, the cross sections have been evaluated by different

authors. The calculations become somewhat simpler if the energy of the

photon, is small enough to neglect the relativistic effects and large

enough to neglect the binding energy of the orbital election. Neglecting

the binding energy of the K-electron, W. Heitler obtained the following

expression for the photoelectric absorption cross-section (in the range 0.1

Mev to 0.35 Mev).

aτk = Φ0Z5 (1/137)44 √ 2(n)7/2 (7)

Where

Φ0 = (8π/3) (e2/m0c2)2=6.651*10-25cm2 (8)

And

n=m0c2/hv (9)

66

Where,

z is the atomic number of the absorber,

e is the charge of the electron,

c is the velocity of light, and

m0 is the rest mass of an electron.

Eq. (7) applies only to the ejection of electros from the K-shell of the

atom, which usually accounts for about 80 per cent of the photoelectric

absorption. In general, aτ depends on Z and hv in the following fashion

aταZ5 (10 a)

α1/(hv)7/2 (10 b)

As the energy of the photon becomes lower, it is not possible to neglect

the binding energy of the K-electron.

b) Compton effect (C.E.): (predominates in the energy range 100 Kev to

1.0 Mev).

This is the process by which the incident photon interacts with a

free electron and is scattered with a lower energy, the rest of the energy

being taken by the recoiling electron. Because the electrons in an atom

are loosely bound and the energies of the incident photons are

comparatively high, we may include the scattering of photos by the

electrons of the atom as Compton scattering. An incident photon of

energy hv strikes a free electron with a rest mass m0. The interaction

results in a scattered photon of energy hv’(<hv) at an angle ө and a

recoiling electron with kinetic energy ke at an angle Φ (Fig. 2). Form the

conservation of momentum and energy using the relativistic expressions,

we obtain

hv/c=(hv/c) cos ө+m0βc (1-β2)-1/2cosΦ (11 a)

67

(hv’/c) sin ө = m0βc(1-β2)-1/2 sin Φ (11 b)

And, hv=hv’+m0c2 [(1-β2)-1/2-1] (11 c)

Where β=v/c, v being the velocity of the electron after the collision.

Elimination Φ and β from the above equations, we get the chance in wave

length given by

λ’-λ = (h/m0c) (1-cosө) (12)

We can establish the following relations by using Eqs. (11a, b, c)

hv'=hv/1+α(1-cosө) (13)

ke=hv-hv'=hv[1-(1/1+α(1-cosө))] (14)

and

cos ө = 1-[2/(1+α)2 tan2 ө+1] (15)

Where α=hv/m0c2, i.e., α is the energy of the incident photon expressed in

units of the rest-mass energy of the electron.

Fig. 2 Compton scattering; the incident photon energy is shared between

the scattered photon of energy hv’ where (v’<v) and an electron.

In order to calculate the Compton scattering cross-section, and the

attenuation coefficients due to the Compton Effect, the problem is to be

treated quantum mechanically, making use of the Dirac equation for the

68

electron. Such calculations have been carried out theoretically by O.

Klein and Y. Nishina. There are many quantities of interest that may be

calculated. Some of these are:

1) eσ = total Compton cross-section for the number of photons

scattered.

2) eσs = Compton cross-section for the energy of the photon scattered,

3) eσa= Compton cross-section for the energy absorbed by the

electrons,

4) eσ2ө = cross-section for the number of photons scattered between 0

and ө0,

5) eσsө0 = cross-section for energy scattered between 0 and ө0, and

6) eөf = cross-section for the number of photos scattered forward.

We shall state the calculated cross section for the first three of them are

related by the following equation.

eσ = eσs + eσa (16)

The theoretical values of eσ and eσs are,

eσ = ¾ Φ0{(a+α/α2) [(2(1+α)/1/2α)-1/α ln (a+2α)] + 1/2αln (1+2α) -

1+3α/(1+2α)2]

And

eσs= 3/8 Φ0 {1/α3 ln (1+2α) + 2(1+α)(2α2-2α-a)/α2(1+2α)2 + 8α2/3(1+2α)3}

(18)

There, as already stated, Φ0 = (8π/3)(e2/m0c2)2 = 6.651*10-25 cm2 and α

= hv/m0c2.

69

The corresponding absorption coefficients µσ, µes, and µσa are

related to sσ, eσs, and eσa in the following manner

σ = (ρNAZ/A) eσ, σs = (ρNAZ/A) eσs, σa = (ρNAZ/A) eσa (19)

The following observations are made from Eqs. (17), (18) and (19) :

i) eσ, eσs, and eσa (cm/electron) are independent of the properties of the

absorber while µσ, µσs, and µσa are functions of the atomic umber of the

material, i.e., the scattering is proportional to Z.

ii) The mass absorption coefficient µσ/ρ given by

σ/ρ =NA (Z/A) eσ (20)

Because for light elements Z/A ~ ½, Eq. (20) implies that the mass

absorption coefficient for a given photon energy is practically constant

for light elements.

iii) The decrease of the total scattering coefficient per electron, eσ, is

slow for photon energies up to 0.5 Mev, but beyond that the decrease is

roughly proportional 1hv.

C) Pair production (P.P.): (possible only when energy is above 1.02

Mev.)

The third most important process by which photons lose there is

electron-positron pair formation. The threshold energy for this process is

2m0c2. It is found that if a photon of energy greater than 1.02 Mev strikes

a foil of high Z, the photon disappears and in its place an electron

positron pair is formed (Fig. 3). If a pair is produced in cloud chamber

and a magnetic field is applied, the electrons and positrons are deflected

in the opposite direction which equal curvature.

70

The conservation of momentum requires the presence of a heavy

body. Actually the pair formation takes place in the filed of the nucleus

and the conservation of energy gives

hv=2m0c2+E++E_+Enuc (21)

where hv=energy of the incident photon,

2m0c2 = energy of the equivalent to the reset mass of the electron

and the positron;

E+, E_, Enuc = the kinetic energies of the positron, electron, and the

recoiling nucleus, respectively.

Because the mass of the nucleus is very large, it takes away a very

small amount of kinetic energy, and so Enuc am be neglected. Thus Eq.

(21) takes the form

hv = 2m0c2 + E++E (22)

which clearly shows that the threshold for pair formation is 2m0c2 or 1.02

Mev.

Fig. 3 Electron-positron pair formation,

Pair production is also possible in the field of light particles, but

the threshold is such cases are higher. The theoretical calculation has

been accomplished by H. Bethe and W. Heilter. The absorption

coefficient aK per atom increase with increasing energy of the photon and

also increase with Z2.

71

CHAPTER - IV

RESULT & DISCUSSION

Table 1 Counts per 60 second for Alanine at 0.662 MeV.

I0 = 6683

Back ground counts: 58

Source used Cs 137

Photo Peak 5.3

Sr. No. Thickness (g/cm2)

Trial I Trial II Mean I/ I I0/I

1

2

3

4

5

0.474

0.548

1.423

1.897

2.371

6678

6300

5969

5860

5778

6670

6306

5975

5878

5760

6674

6303

5972

5869

5769

6616

6245

5914

5811

5711

1.01

1.07

1.13

1.15

1.17

72

Figure 1.Plot of I0/I Vs thickness t for Alanine at 0.662 MeV.

73

Table 2 Counts per 60 second for Alanine at 1.17 MeV.

I0 = 1988

Back ground counts: 38

Source used Co 60

Photo Peak 6.1

Sr. No. Thickness (g/cm2)

Trial I Trial II Mean I/ I I0/I

1

2

3

4

5

0.474

0.548

1.423

1.897

2.371

1976

1932

1860

1816

1780

1960

1830

1862

1810

1782

1968

1931

1861

1813

1781

1930

1893

1823

1775

1743

1.03

1.05

1.09

1.12

1.14

74

Figure 2.Plot of I0/I Vs thickness t for Alanine at 1.17 MeV

75

Table 3 Counts per 60 second for Alanine at 1.280 MeV.

I0 = 17022

Back ground counts 58

Source used : Na22

Photo Peak 9.1

Sr. No Thickness (g/cm2)

Trial I Trial II Mean I/ I I0/I

1

2

3

4

5

0.474

0.548

1.423

1.897

2.371

16752

16420

16122

15670

14993

16740

16430

16110

15678

14985

16746

16425

16116

15674

14989

16688

16367

16058

15616

14931

1.02

1.04

1.06

1.09

1.14

76

Figure 3 .Plot of I0/I Vs thickness t for Alanine at 1.280 MeV.

77

Table 4 Counts per 60 second for Alanine at 1.33 MeV.

I0 = 2536

B. C Background count: 40

Source used: Co60

Photo peak: 7.8

Sr No Thickness (g/cm2)

Trial I Trial II Mean I/ I I0/I

1

2

3

4

5

0.474

0.548

1.423

1.897

2.371

2532

2430

2415

2300

2288

2520

2434

2405

2308

2280

2526

2432

2410

2304

2284

2486

2392

2370

2264

2244

1.02

1.06

1.07

1.12

1.13

78

Figure 4.Plot of I0/I Vs thickness t for Alanine at 1.33 MeV.

79

Table 5: Linear attenuation coefficient μ (cm-1) and mass attenuation coefficient μ/ρ (cm2/g) of Alanine absorber at Photon energies 0.662, 1.170, 1.280 and 1.330 MeV

_______________________________________________

Sr. No. Energy MeV μ (cm-1) μ/ρ (cm2/g)

__________________________________________________

1 0.662 0.121 a 0.084 a

0.119 b 0.083 b

-1.256 c -1.205 c

2 1.170 0.088 a 0.061 a

0.091 b 0.063 b

3.297 c 3.174 c

3 1.280 0.087 a 0.061 a

0.086 b 0.060 b

-1.162 c -1.666 c

4 1.330 0.085 a 0.059 a

0.085 b 0.059 b

0.000 c 0.000 c

___________________________________________________

a (experimental)

b (Hubbell and Seltzer) values.

c (Percentage deviation)

80

Table 6 Linear attenuation coefficient for Alanine at 0.662,

1.170, 1.280 and 1.330 MeV.

Energy MeV μ (cm-1)

0.662

1.170

1.280

1.330

0.121 a

0.119 b

0.088 a

0.091 b

0.087 a

0.086 b

0.085 a

0.085 b

a (experimental)

b (Hubbell and Seltzer) values.

81

Figure 5 Linear attenuation coefficients for Alanine at 0.662, 1.170,

1.280 and 1.330 MeV.

82

Table 7 Mass attenuation coefficient for Alanine at 0.662, 1.170, 1.280 and 1.330 MeV.

Energy MeV μ/ρ (cm2 /gm)

0.662

1.170

1.280

1.330

0.084 a

0.083 b

0.061 a

0.063 b

0.061 a

0.060 b

0.059 a

0.059 b

a (experimental)

b (Hubbell and Seltzer) values.

83

Figure 6 Mass attenuation coefficients for Alanine at 0.662, 1.170,

1.280 and 1.330 MeV.

84

Table 8 Total attenuation cross sections for Alanine at 0.662, 1.170, 1.280 and 1.330 MeV.

Energy MeV σ tot (barn/molecule)

Experimental Theoretical

(a) (b)

0.662

1.170

1.280

1.330

12.428 12.280

9.025 9.321

8.877 9.025

8.729 8.729

Figure 7 Total attenuation cross sections for Alanine at 0.662, 1.170,

1.280 and 1.330 MeV.

85

Table 9 Effective atomic number (Zeff) for Alanine at 0.662, 1.170, 1.280

and 1.330 MeV.

Energy KeV Zeff

662

1170

1280

1330

3.6684

3.6494

3.6498

3.6500

Figure 8 Effective atomic number (Zeff) for Alanine at 0.662, 1.170,

1.280 and 1.330 MeV.

Table 10 Electron densities for Alanine at 0.662, 1.170, 1.280 and 1.330 MeV.

86

Energy KeV Ne (10 23 g-1)

662

1170

1280

1330

3.2232

3.2066

3.2069

3.2071

Figure 9 Electron densities for Alanine at 662, 1170, 1280 and 1330 keV.

* Aeff i.e. Effective atomic weight = ______A_______________

Total number of Molecules

87

Present in the sample

Aeff = 89.1

13

= 6.8538

* < Z > Mean Atomic number = _________Z___________

Total number of Molecules

Present in the sample

< Z > = 48

13

= 3.6923

* ρ Density of Alanine = 1.437 gm/cm3

Molar Extinction coefficient = 1/ln 10 NA

Table 11 Molar Extinction coefficient for Alanine at 0.662, 1.170, 1.280 and 1.330 MeV.

88

Energy MeV (cm2 mol-1)

Experimental Theoretical

(a) (b)

0.662

1.170

1.280

1.330

3.250 3.217

2.360 2.437

2.321 2.437

2.282 2.282

Figure 10 Molar Extension coefficient for Alanine at 0.662, 1.170,

1.280 and 1.330 MeV.

CHAPTER V

89

Conclusions :-

1. For (linear attenuation coefficient):- From Fig.(5) in chapter IV

we can conclude that as energy increases the value of linear

attenuation coefficient goes on decreasing. For low energy region

(i.e.0.662 MeV) there is a large value of linear attenuation

coefficient but as energy increases there is sudden decrease in

linear attenuation coefficient ( cm-1) value in the energy region

(1.17-1.33 MeV). After this the value of decreases slowly and

then nearly remains constant.

2. For /ρ (mass attenuation coefficient):- From fig (6) in chapter IV

we can also seen that as energy increase the value of mass

attenuation coefficient goes on decreasing. For low energy region

(i.e.0.662 MeV) there is a large value of mass attenuation

coefficient but as energy increases there is a sudden decrease in

mass attenuation coefficient (/ρ cm2/g) value in the energy region

(1.77-1.33 MeV). After this the value of /ρ decrease slowly and

then nearly remains constant.

3. For σ tot (total attenuation cross-section):- From fig (7) in chapter

IV we can also seen that as energy increase the value of total

attenuation cross-section goes on decreasing. For low energy

region (i.e.0.662 MeV) there is a large value of total attenuation

cross-section but as energy increases there is a sudden decrease in

total attenuation cross-section (σ tot barn/molecule) value in the

energy region (1.77-1.33 MeV). After this the value of σtot

decrease slowly and then nearly remains constant.

4. For Zeff. (effective atomic number) from fig. (8) From chapter IV

we can conclude that at lower energy i.e. (0.662 MeV) there is a

90

large value of Zeff it is (3.6684) but as energy increases then there

is no considerable change is observed in our reading. For higher

energies the value of Zeff remains nearly constant.

5. For Ne (electron density): From fig. (9) in chapter IV we can

conclude that at lower energy i.e.(0.662MeV) there is a large

value of Ne It is 3.2232 x 10 23 g -1 but as energy increases then

there is no considerable change is observed in our reading. For

higher energies the value of Ne remains nearly constant.

6. For (molar extinction coefficient) From fig (10) in chapter IV we

can conclude that at lower energy i.e. (0.662 MeV) there is a large

value of . It is 3.250 but as energy increases then there is no

considerable change is observed in our reading .For higher

energies the value of remains nearly constant.

7. (Z):- Mean atomic number for Alanine is (3.6923)

8. Density of Alanine is:- (1.437)gm/cm3

9. The effective atomic number Zeff and the corresponding effective

electron density Ne of Alanine have been calculated in the energy

region from (5-1500kg.) using with XCOM programe.

10. The ratio Zeff/Aeff was (0.5) for Alanine containing (H, C, N & O)

elements in the energy region (5-1500) kev. For example if we

consider Zeff value of energy 0.662 is 3.6684 and the Aeff value of

it is = 6.8538 than we have Zeff/Aeff = 3.6684/6.8538 = 0.5

11. It has been observed that the same value of total attenuation

cross-section for all the compounds of the same molecular weight

but different chemical structure at a given energy.

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