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Chapter 28 Lecture

Nuclear Physics

© 2014 Pearson Education, Inc.

Nuclear Physics

• How are new elements created?

• What are the natural sources of ionizing

radiation?

• How does carbon dating work?


Be sure you know how to:

• Use the right-hand rule for magnetic force to

determine the direction of the force exerted by a

magnetic field on a moving charged particle

(Section 17.4).

• Relate mass to energy using the special theory

of relativity (Section 25.8).


Relativistic energy


Relativistic Energy


What's new in this chapter

• In this chapter, we investigate several questions

about the nucleus:

– What is the structure of the nucleus, and

which processes do nuclei undergo?

– Do these processes occur only in stars or in

huge particle accelerators, or do they happen

every day and perhaps even in our bodies?


Becquerel and the emissions from uranyl

crystals

• Becquerel found that uranium crystals that had

not been exposed to sunlight formed images on

photographic plates.

– The uranium emitted radiation without an

external source of energy.


Observational experiment


Pierre and Marie Curie and the particles

responsible for Becquerel's rays

• Chemical changes or changes in the amount of

light shining on a sample did not lead to

changes in the amount of radiation produced by

uranium salts.

– These findings suggested that the electrons

in the atoms were not responsible for the

rays.

– Marie and Pierre Curie concluded that the

Becquerel rays must come from the nuclei of

atoms.


Rutherford and experiments investigating

the charge of emitted particles

• Rutherford covered a uranium sample with thin

aluminum sheets to investigate how metal layers

affected the amount of radiation.


Testing experiment


Alpha particles, beta rays, and gamma rays

• Rutherford found positively charged particles

with a mass-to-charge ratio twice that of a

hydrogen ion; they were called alpha rays or

alpha particles.

• Negatively charged particles had the same

mass-to-charge ratio as that of the electron; they

were called beta rays.

• Neutral radiation was thought to consist of high-

energy electromagnetic waves, called gamma

rays.


The early model of the nucleus

• The nucleus of an atom is made of positively

charged alpha particles and negatively charged

electrons.

– When a nucleus contains a large number of

alpha particles, they start repelling each other

more strongly than the electrons can attract

them, and the alpha particles leave the

nucleus.

– This leaves behind electrons that repel each

other; thus beta rays are emitted.

– The nucleus is left in an excited state and

emits a high-energy photon, a gamma ray. © 2014 Pearson Education, Inc.

Problem with the early model of the nucleus

• A hydrogen atom is lighter than an alpha

particle.

– What, then, is the composition of its nucleus?


Size of the nucleus: Too small for an

electron

• We can use the uncertainty principle and the

size of the nucleus to show that our current

models would result in atoms that rapidly lose

their electrons.


The search for a neutral particle

• An alpha particle has the charge of two protons

but four times the mass of a proton; thus it

cannot be made of two protons.

– In 1920, Rutherford suggested a neutral

particle with the approximate mass of a

proton.

– In 1928, Bothe and Becker took the initial

step in this search.


The neutral radiation is not a gamma-ray

photon

• By comparing the energies and momenta of the

particles knocked out of different atoms,

Chadwick determined that the particles were

uncharged particles with a mass approximately

equal to that of the proton.


Revising ideas of the structure of the

nucleus

• A new model of nuclear

constituents evolved

that involved protons

and neutrons.

– The protons

accounted for the

electric charge of the

nucleus.

– The uncharged

neutrons accounted

for the extra mass.


One atomic mass unit


Atomic Mass

• The atomic masses are specified in terms of the atomic

mass unit u, defined such that the atomic mass of

isotope 12C is exactly 12 u.

1 u = 1.6605 × 10–27 kg

• The energy equivalent of 1 u of mass is

• To find the energy equivalent of any atom or particle

whose mass is given in atomic mass units we can use


Atomic Mass

• We can write 1 u in the following form as well:

• MeV/c2 are units of mass. The energy equivalent

of 1 MeV/c2 is 1 MeV.


Isotopes

• Atoms of a particular element with different

numbers of neutrons are called isotopes of that

element.

– The electronic structure of an element's

isotopes is the same, which means their

chemical behaviors are almost identical.

– However, the nuclei behave quite differently.


Conceptual Exercise 28.1

• Determine the number of protons and neutrons

in each of the following nuclei:

A.

B.

C.

D.

E.

F.


Tip


Nuclear force and binding energy

• How can protons stay bound

together when they repel

each other so strongly?


Nuclear force

• Some attractive force must balance this

electrical repulsive force and must attract

neutrons as well; it has to be an attractive force

for both protons and neutrons.

– We call this attractive force a nuclear force.

– The nuclear force must weaken to nearly zero

extremely rapidly with increasing distance

between nucleons.

– If it didn't, then nuclei of nearby atoms would

be attracted to each other, clumping together

into ever-larger nuclei.


Nuclear binding energy

• The binding energy of the nucleus is the energy

that must be added to the nucleus to separate it

into its component protons and neutrons.

• The nucleus is a bound system, so its nuclear

potential energy plus electric potential energy

plus kinetic energy of the protons and neutrons

must be negative.


Binding energy


The nuclear binding energy is computed by considering the mass

difference between the atom and its separate components, Z

hydrogen atoms and N neutrons:

30

Binding Energy


Example Finding the binding energy of iron

What is the nuclear binding energy of 56Fe to the

nearest MeV?

• Atomic mass of 56Fe as 55.934940 u. Iron has

atomic number 26, so an atom of 56Fe could be

separated into 26 hydrogen atoms and 30

neutrons.

• The mass of the separated components is more

than that of the iron nucleus; the difference gives

us the binding energy.


Example 30.1 Finding the binding energy of

iron (cont.)

SOLVE We solve for the binding energy using

Equation 30.4. The masses of the hydrogen atom

and the neutron are given in Table 30.2. We find


Example 30.1 Finding the binding energy of

iron (cont.)

ASSESS The difference in mass between the

nucleus and its components is a small fraction of

the mass of the nucleus, so we must use several

significant figures in our mass values. The mass

difference is small—about half that of a proton—

but the energy equivalent, the binding energy, is

enormous.


Forces and Energy in the Nucleus

• The strong nuclear force is the force that

keeps the nucleus together.

1. It is an attractive force between any two

nucleons.

2. It does not act on electrons.

3. It is a short-range force, acting only over

nuclear distances. We see no evidence for

the nuclear forces outside the nucleus.

4. Over the range where it acts, it is stronger

than the electrostatic force that tries to push

two protons apart.



• A nucleus with too many

protons will be unstable

because the repulsive

electrostatic forces will

overcome the attractive

strong forces.

• Because neutrons

participate in the strong

force but exert no

repulsive forces, the

neutrons provide the

extra “glue” that holds

the nucleus together. © 2015 Pearson Education, Inc.


• In small nuclei, one neutron per proton is

sufficient for stability, so small nuclei have N ≈ Z.

• As the nucleus grows, the repulsive force

increases faster than the binding energy, so

more neutrons are needed for stability.



• Protons and neutrons have quantized energy

levels like electrons. They have spin and follow

the Pauli exclusion principle.

• The proton and neutron energy levels are

separated by a million times more energy than

the energy separation of electron energy levels.


Low-Z Nuclei

• Low-Z nuclei (Z < 8) have few protons, so we

can neglect the electrostatic potential energy

due to proton-proton repulsion.

• In this case, the energy levels of protons and

neutrons are essentially identical.


39

Low-Z Nuclei


Low-Z Nuclei

• The nuclear energy-level diagram of 12C, which

has 6 protons and 6 neutrons, shows that it is in

its lowest possible energy state


Low-Z Nuclei

• 12B and 12N could lower their energies in a

process known as beta decay—where a proton

turns into a neutron or vice versa.


High-Z Nuclei

• In a nucleus with many protons, the increasing

electrostatic potential energy raises the proton

energy levels but not the neutron energy levels.

• If there were neutrons in energy levels above

vacant proton levels, the nucleus would lower its

energy by changing neutrons into protons, and

vice versa.

• The net result is that the filled levels for

protons and neutrons are at just about the

same height.

• Because neutron energy levels start at a lower

energy, more neutron states are available.


43

High-Z Nuclei


Binding Energy

• As A increases, the nuclear binding energy

increases because there are more nuclear

bonds.

• A useful measure for comparing one nucleus to

another is the quantity B/A called the binding

energy per nucleon.


Binding energy per nucleon


46

Nuclear Stability


Nuclear Stability • Graphically, the stable nuclei cluster very close to the

line of stability.

• There are no stable nuclei with Z > 83 (bismuth). Heavier

elements (up to Z = 92, uranium) are found in nature but

they are radioactive.

• Unstable nuclei are in the bands along both sides of the

line of stability.

• The lightest elements with Z < 16 are stable when N ≈ Z.

• As Z increases, the number of neutrons needed for

stability grows increasingly larger than the number of

protons.

Binding Energy

• The line connecting the points on this graph is

called the curve of binding energy


Binding Energy

• If two light nuclei can be joined together to make

a single, larger nucleus, the final nucleus will

have a higher binding energy per nucleon.

• Because the final nucleus is more tightly bound,

energy will be released in this nuclear fusion

process.

• Nuclear fusion of hydrogen to helium is the basic

reaction that powers the sun.


Binding Energy

• Nuclei with A > 60 become less stable as their mass

increases because adding nucleons decreases the

binding energy per nucleon.

• Alpha decay is a basic type of radioactive decay that

occurs when a heavy nucleus becomes more stable by

ejecting a small group of nucleons in order to decrease

its mass, releasing energy in the process.

• Nuclear fission is when very heavy nuclei are so

unstable that they can be induced to fragment into two

lighter nuclei.


Binding Energy

• The collision of a slow-moving neutron with a 235U nucleus causes the reaction

• 236U is so unstable that it immediately fragments,

in this case into two nuclei and two neutrons. A

great deal of energy is released in this reaction.


Representing nuclear reactions

• The advantage of writing nuclear reactions as

shown here is that atomic masses (found in

atomic mass tables) can be used to analyze the

energy transformations that occur during the

reactions:


Rules for nuclear reactions


Tip


Quantitative Exercise 28.3

• Determine the missing products in the following

reactions:


Testing experiment


Energy conversions in nuclear reactions


Binding energy and energy release

• The higher the binding energy per nucleon, the

more energy needed to split the nucleus into its

constituent protons and neutrons.


Binding energy and energy release

• The graph predicts:

– When two small nuclei combine, energy should be

released.

– When a large nucleus breaks apart, energy should be

released.


Fusion and chemical elements

• Fusion occurs naturally in stars; it requires high

heat and high pressure to overcome the

repulsion from the electric charges.


Fusion and chemical elements

• Supernova explosions contribute to the chemical

composition of the universe.

– The elements lighter than iron that are

produced in stars' cores before the explosion

are ejected into space.

– The elements heavier than iron that are

produced during the explosion are then

ejected into space.



• The energy released by the Sun comes from

several sources, including the proton-proton

chain of fusion reactions:

• Determine the energy released in this chain of

reactions in MeV. Use the masses

, , and

to determine the rest energy

converted to other forms.


Fission and nuclear energy


Bohr's liquid drop model of the nucleus

• Frisch and Meitner decided that Bohr's liquid

drop model of a nucleus could explain the

observation of fission.

– Surface tension holds a water drop together;

likewise, the nuclear forces hold the nucleons

together.

– The protons repel each other and overwhelm

the effect of the "surface tension."

– The nucleus can then stretch itself and divide

into two smaller pieces.


Alpha decay

• When one of the alpha particles leaves, this

emission reduces the number of protons in the

original nucleus as well as the electric repulsion

between the remaining protons.


68

Nuclear decay modes


Text: p.

985


• Determine the kinetic energy of the product

nuclei when polonium-212 undergoes alpha

decay. The masses of the nuclei involved in the

decay are ;

, and .


Beta decay

• During beta decay, a particular element is

transformed into an element with a Z number

that is larger by 1.


Problems with beta decay

• The problem with spin conservation:

– In beta decay, the spin quantum number was

not conserved.

• The problem with energy conservation:

– The total energy of the products was always

observed to be less than the total energy of

the reactants.


Beta decay

• Wolfgang Pauli proposed an explanation for

beta decay that did not require abandoning

energy conservation or spin number

conservation.

– He hypothesized that some unknown particle

carried away the missing energy and

accounted for the discrepancy in spin

number.

– This particle had zero electric charge, zero

mass, and a spin number of either +1/2 or

–1/2.

– Enrico Fermi called the particle a neutrino,

meaning "little neutral one." © 2014 Pearson Education, Inc.

Beta-minus and beta-plus decay


75

SYNTHESIS 30.1 Nuclear decay modes


Text: p.

985

Gamma decay

• After alpha or beta

decay, the nucleus can

be left in an excited state

from which it then emits

one or more photons to

return to its ground state.


Gamma Decay

• Gamma decay occurs when a proton or neutron

undergoes a quantum jump.



• The following nuclei undergo different types of

radioactive decay. Determine the daughter

nucleus for each and write an equation

representing each decay reaction.

– alpha decay

– beta-minus decay

– beta-plus decay (produces a positron)


Half-life

• Using a particle detector such as a Geiger

counter, we can measure the number of nuclei

that decay in a short time interval and determine

the number N of radioactive nuclei that remain in

the sample as a function of time.


Half-life


Half-lives and decay constants of some

common nuclei


Determining the source of carbon in plants

• The photosynthesis process in plant growth may

be summarized as follows:

6CO2 + 6H2O + sunlight → C6H12O6 + 6O2

– Some CO2 in the atmosphere, including the

carbon-11 isotope, is synthesized by plants.

– The naturally occurring carbon isotope

carbon-11 is radioactive, with a half-life of 20

minutes.


Decay rate (activity) A


Exponential decay


Decay rate and half-life

• At time t = T (one half-life), the number N of

radioactive nuclei remaining is one-half the

number N0 at time zero:

• If the decay constant is large, then the material

decays rapidly and consequently has a short

half-life T.


Radioactive dating

• Archeologists and geologists are interested in

determining the age of a radioactive sample

from the known fraction N/N0 of radioactive

nuclei that remain in the sample:

• In this equation, T is the half-life of the

radioactive material and t is the sample's age

when N radioactive nuclei remain.


Tip


Carbon dating

• Any plant or animal that metabolizes carbon

incorporates about one carbon-14 atom into its

structure for every 1012 carbon-12 atoms it

metabolizes.

– Carbon is no longer metabolized by the

organism after death, so the carbon-14 starts

to transform into nitrogen-14.

– After 5700 years, the carbon-14

concentration decreases by one-half.

– A measurement of the current carbon-14

concentration indicates the age of the

remains. © 2014 Pearson Education, Inc.

Example 28.11

• A bone found by an archeologist contains a

small amount of radioactive carbon-14. The

radioactive emissions from the bone produce a

measured decay rate of 3.3 decays/s. The same

mass of fresh cow bone produces 30.8

decays/s. Estimate the age of the sample.


Radioactive decay series


Ionizing radiation and its measurement

• Ionizing radiation's effects on living organisms

are classified into two categories: genetic

damage and somatic damage.

– Genetic damage occurs when the DNA

molecules in the reproductive cells are

altered by the radiation. These genetic

changes are passed on to future generations.

– Somatic damage involves cellular changes to

all parts of the body except the reproductive

cells.


Absorbed dose


Relative biological effectiveness (RBE)


Dose or dose equivalent



• In a typical chest X-ray, about 10 mrem

(10 x 10–3 rem) of radiation is absorbed by about

5 kg of body tissue. Each of the X-ray photons

used in such exams has approximately

50,000 eV of energy. Determine about how

many ions are produced by this X-ray exam.


Natural sources of ionizing radiation

• Radioactive elements in the Earth's crust include

uranium-238, potassium-40, and radon-226.

• Foods may contain radioactive isotopes.

• Cosmic rays are elementary particles moving at

almost the speed of light. The original source of

cosmic rays was primarily supernova explosions

of stars in our galaxy.


Human-made sources of ionizing radiation


Summary


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