physics week 16(sem. 2) - st. francis preparatory schoolenergy per nucleon versus nucleon number...

Ms. N. May ABC Math Student Copy

Physics Week 16(Sem. 2) Name____________________________

The Nuclear Chapter Summary

Nuclear Structure

Atoms consist of electrons in orbit about a central nucleus. The electron orbits are quantum mechanical in nature. The nucleus consists of protons and neutrons, collectively referred to as nucleons. The neutron was discovered in 1932 by James Chadwick. It was found to have no electrical charge and a mass slightly larger than that of a proton (almost the same). The number of protons in the nucleus of an atom is different in different elements, it is given by the atomic number (Z). In an electrically neutral atom, the number of protons are equal to the number of electrons. The number of neutrons in the nucleus is N. The total number of neutrons and protons in the nucleus is called the atomic mass number (A), this is because the total mass is approximately equal to the neutrons and protons together. Therefore, the atomic mass number is the number of protons and neutrons added together

(A=N+Z). For a proton the symbol is typically , the

neutron is denoted , and the electron is .

Isotopes are elements that contain the same number of protons and different numbers of neutrons in the nuclei. Carbon for example has two stable isotopes; the most common atom of carbon has 6 protons, 6 neutrons and 6 electrons (98.9%). The other common stable isotope of carbon has 6 protons, 7 neutrons, and 6 electrons (1.1%). The atomic masses in the periodic table are an average of the most common stable isotopes of the elements.

The protons and neutrons are clustered in the nucleus in a nearly spherical arrangement. Experiment shows that the radius of the nucleus (r) depends on atomic number (A) and can be calculated in meters by

1.2 10 /

Using this equation and the equation for density, it can be found that the density of differing atoms is approximately the same. Therefore, the differences in material densities arise mainly because of the difference in how closely the atoms are packed to themselves, not the nuclear density.

Strong Nuclear Force & Stability of Nucleus

Two positively charged objects or particles would typically have strong repulsive forces. However, the nucleus can stay intact with many positive charges residing within a small region together. There must be some attractive force that overcomes the electrical repulsion to allow for a stable nucleus. The gravitational force is too weak (mass is small), so there must be some other force. This force is called the strong nuclear force and is one of the three fundamental forces (also gravitational and electroweak forces). Much is known about the strong nuclear force.

The strong nuclear force is almost independent of electrical charge. At a set distance of separation, the nuclear force of attraction between two protons, two neutrons or between one proton and one neutron. The range of effectiveness of the force is very short, it is very strong at distances on the order of 10‐15 m and essentially zero at larger distances.

The strong nuclear force only acts over very short distances, it is this that makes it so important in nuclear stability. For the nucleus to be stable, the electrostatic repulsion between protons, must be balanced by the strong nuclear force. Figure 31.2 shows the line for N=Z and the belt of stability. For all elements (few exceptions), the belt of stability range is mostly around 2A (twice the total of protons). For the most part all elements with 83 protons and more at unstable nuclei.

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Mass Defect

Because of the strong nuclear force, the nucleus is help together. Therefore, energy is required to separate a stable nucleus into its constituent protons and neutrons. The more stable the nucleus is the more energy needed to break it apart. The required energy to do this is called the binding energy. It follows Einstein’s famous equation

∆

Where E is the binding energy (J), m is the mass in kg, c is the speed of light (m/s). See example 2. Knowing the mass of the hydrogen atom (containing only a proton) is 1.0073 amu and has a mass of 1.6726x10‐27kg, thus 1 amu=1.6605x10‐27kg. Using this and then solving the equation above for the energy equivalent of 1 amu, you would obtain

∆ ∆ 1.6605 10 272.9979 10

Therefore the energy equivalent to 1 amu mass defect is 1.4924x10‐10J. Or in electron volts (1eV=1.6022x10‐19J) thus the energy equivalent of 1 amu is 931.5 MeV. See example 3.

If the binding energy for different atoms were to be analyzed it would be important to do it on a per nucleon basis. As can be seen in the graph of binding energy per nucleon versus nucleon number (A), the maximum binding energy per nucleon is approximately 8.7 MeV. Helium (A=4) has a binding energy per nucleon very close to the maximum at about 7MeV/nucleon. Also, it is important to note the binding energies per nucleon peak at about Fe and As and then gradually decrease continually. After Bi (bismuth) the nucleus gets so massive that there is insufficient binding energy to hold the nucleus together leading to unstable and hence radioactive nuclei.

Radioactivity

When an unstable or radioactive nucleus disintegrates spontaneously, certain kinds of particles and/or high‐energy photons are released. These are released particles/photons are called rays. There are three

commonly released rays; alpha rays (α), beta rays (β), and gamma rays (γ). They were given these names in order of their penetrating power (following the Greek alphabet), thus alpha particles penetrate the least and gamma the most. The process that produces the rays has to follow the laws of physics (cons. Laws). To all of the previously learned conservation laws (linear momentum, mass/energy, electrical charge, angular momentum) another conservation law applies, this is conservation of nucleon number. This last conservation law was determined after studying disintegrated nuclei where it was found the number of nucleons after was equal to the original number of nucleons.

A simple experiment can be setup to observe the three types of naturally occurring radioactivity. A magnetic field could be setup which will deflect only the charged particles resulting in a separation of the charged particles from the uncharged particles.

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Analyzing the previous image the alpha particles are deflected toward the top of the page, the beta particles were deflected toward the bottom of the page, and the gamma rays were unaffected. Therefore, alpha and beta rays were discovered to be charged particles. Meanwhile, gamma rays were found to be uncharged rays.

Alpha Decay

Alpha decay is the result of an unstable nucleus emitting an alpha particle. The alpha particle has a positive charge of +2e and a nucleon number of A=4. This is the nucleus of a Helium atom, which was previously found to be very stable compared to other nuclei. An example of an alpha decay disintegration would be:

This is the alpha decay that results from a Uranium nucleus. The original nucleus is commonly referred to as the parent nucleus (P). The remaining nucleus after the disintegration is referred to as the daughter nucleus (D). When the parent and daughter nuclei are different, this process converts one element into another and is called transmutation. Note that the above alpha decay is consistent with conservation of charge and nucleon number (top and bottom numbers). When a nucleus releases an alpha particle the nucleus also releases heat, this is in part the source of heat for Earth. See Example 4. It is important to note that the released energy appears as kinetic energy of the recoiling Thorium nucleus and alpha particle (not including some carried away as a gamma ray). Alpha decay is used commonly in smoke detectors.

Beta Decay

Beta particles have an opposite charge compared to alpha particles, they are negative. Experiment shows that these particles are electrons. Consider the following beta decay:

Beta decay, similarly to alpha decay, results in the transmutation of one element into another. The above equation obeys the conservation of nucleon number and charge. It has been found that the emission of the electron is the result of a neutron decaying into a proton and an electron. The number of nucleons remained unchanged, while the number of protons increased by one (neutron into proton). The charge was conserved since a neutral particle decayed into a positive and negative particle. This type of beta decay

is called β‐ decay. There is also β+ decay, the particle emitted in this case is called a positron (or a positive charge, with the mass of an electron). The nucleon number remains unchanged while the nucleus decreases by one proton. This positron is the result of a proton transforming into a neutron.

Gamma Decay

The nucleus, like orbiting electrons, exist only in discrete energy states or levels. When the nucleus changes from a higher energy state (denoted by *) to a lower energy state, a photon is emitted. The process is similar to the photon emission that leads to the bright line emission spectrum. With nuclear energy levels, however, the photon has a much higher energy and is

called specifically the gamma ray (γ). The process for gamma decay can be seen below:

Gamma decay does not cause a transmutation of one element into another. See Example 7 for Gamma decay. Gamma knife surgery is a very promising surgical technique for the removal of masses/tumors in the brain. The intense concentration of gamma rays meet at the exact location of the problem and this intensity will destroying the target and leaving the healthy tissue unharmed (b/c it is the combination of small dose rays). This is noninvasive and reduces hospital stays by about

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90%, allowing patients to return to work within a few days.

The Neutrino

When a beta particle is emitted from an unstable nucleus, energy is simultaneously released. Experiments show that the kinetic energy and mass defect during this process does not completely account for the total energy lost. Wolfgang Pauli proposed that part of the energy is carried away by another particle that is emitted with the beta particle, called the neutrino. The existence of the neutrino was confirmed

in 1956, it is represented by the Greek symbol (ν‐nu). Therefore the beta decay of thorium (Th) should be:

The bar over the neutrino is to indicate an antimatter

neutrino or antineutrino. A normal neutrino (ν without a bar over it) is emitted when Beta positive decay occurs. Currently, there are some thoughts that the neutrino may actually have some mass but this has not been proven. If the mass is zero then it travels at the speed of light. Also, the neutrino has no electrical charge and interacts too weakly with matter to be detected easily. The emission of neutrinos and beta particles involves a force called the weak nuclear force (much weaker than the strong force). It is known, now, that the weak nuclear force and the electromagnetic force are two different manifestations of a single, more fundamental force called the electroweak force. The electroweak force, gravitational force, and the strong nuclear force and the three fundamental forces in nature.

Radioactivity

Knowing which nucleus in a group of nuclei will disintegrate at a given time cannot be known; random disintegrations will occur randomly. As time passes, the number (N) of parent nuclei decreases. The N will smoothly decrease and approach zero as time passes on. The half life (T1/2) of a radioactive isotope is the time required for one‐half of the nuclei present to

disintegrate. For example, radium ( ) has a half life of 1600 years so it takes this amount of time for one half of the given quantity of this isotope to disintegrate. In another 1600 years the half of the original that remains will be reduced to ¼ of the original sample size. The value of the half life depends on the radioactivity of the nucleus. Values range from milliseconds to thousands of years.

The activity of a radioisotope is the number of disintegrations per second that occur. The activity can be obtained by dividing the change in the number of

nuclei (ΔN) by the time interval during which the

change takes place (Δt). The equation below can be used to determine the decay constant (λ):

ΔΔ

λ

Where N is the number of radioactive nuclei remaining. The SI unit of radioactivity is the Becquerel (Bq), one Bq is equal to 1 disintegration per second. It can also be measured in the curie (Ci) where 1 Ci=3.70x1010 Bq. The amount of radium put into a watch to make it glow in the dark has an activity of about 4x104 Bq, while the activity used in radiation therapy is about a billion times greater. If the activity of a nucleus is known then the half life can be calculated, or visa‐versa. Therefore the resulting equation is:

/0.693λ

Where T1/2 is the half life and λ is the activity of an elements nucleus. See example 9.

Radioactive Dating

If an object contains radioactive nuclei when it is formed, then the decay of these nuclei marks the passage of time like a clock (half of the nuclei decay for each half life that passes). If the half life is known, a measurement of the ratio of the nuclei present today can be compared to the nuclei present today and give the age of the sample. The most accurate way of determining the number of radioactive nuclei present today would be to use a mass spectrometer. See example 10 for the dating of a living organism.

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Radioactive Decay Series

When an unstable parent nucleus decays, the resulting daughter nucleus is sometimes also unstable. If so, the daughter nucleus then decays and produces another daughter nucleus. The sequential decay of one nucleus after another is called a radioactive decay series. The following equation is for uranium:

As the graph representing the possible decay series of uranium indicates there are many possible branches for intermediate species. Ultimately, however, the series

ends with lead ( ), which is stable. See the possible branches in the graph below:

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N. M

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Name: ____________________________________________

Questions 1 through 4 refer to the following:

The two equations below are nuclear equations:

27 4 30 Al + He ‡‡ˆ P + X + energy 13 2 15

30 30 P ‡‡ˆ Si + Y + energy 15 14

271) The number of neutrons in the nucleus of Al is 13

A) 40 B) 27 C) 13 D) 14

2) In the second equation, particle Y isA) a neutron B) a positron C) an electron D) an alpha particle

3) In the first equation, particle X isA) a neutrino B) a positron C) a neutron D) an electron

304) Compared to the mass of the P, the sum of the masses of 1530 Si + Y is14

A) the same B) more C) less

Questions 5 and 6 refer to the following:

When nitrogen is bombarded with protons, the first reaction 14 1 15that occurs is N + H ‡‡ˆ O + X. The oxygen produced is 7 1 8radioactive, with a half-life of 0.10 second, and decays in 15 15the following manner: O ‡‡ˆ N + Y. 8 7

5) In the first reaction, X representsA) an alpha particleB) a gamma photon

C) a neutronD) a beta particle

6) In the second reaction, Y representsA) an electronB) a proton

C) a positronD) a neutron


The following represents a nuclear equation.

30 A 0 P ‡‡ˆ Si + X 15 Z +1

7) What is the value of A in the equation?A) 28B) 30

C) 31D) 29

8) In the equation, X representsA) a gamma photonB) a proton

C) a positronD) an electron

9) Which force between the protons in a helium atom will havethe greatest magnitude?A) magnetic forceB) electrostatic force

C) nuclear forceD) gravitational force

10) Approximately how much energy would be generated if the mass 2in a nucleus of a H atom were completely converted to energy? 1 2[The mass of H is 2.0 atomic mass units.] 1

A) 9.3 x 102 MeV B) 1.9 x 103 MeV C) 1.5 x 10-10 J D) 3.2 x 10-19 J

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11) Moderators are used to slow neutrons down in a nuclearreactor in order toA) achieve critical massB) remove radioactive impurities in the coreC) improve the probability of fissionD) reduce nuclear reactions

12) The total number of neutrons in the nucleus of any atom isequal to theA) mass number of the atomB) mass number minus the atomic numberC) atomic number minus the mass numberD) atomic number of the atom

Questions 13 through 15 refer to the following:

The information below represents a nuclear reaction.

3 1 4 H + H ‡‡ˆ He + energy 1 1 2The masses of the nuclei are: 1 H = 1.00813 u (amu) 1 3 H = 3.01695 u (amu) 1 4 He = 4.00388 u (amu) 2

13) How much energy is released during the reaction?A) 0.021 MeVB) 30.0 x 10-19 MeV

C) 19.7 MeVD) 2.00 MeV

14) This reaction is an example ofA) fissionB) alpha decay

C) fusionD) beta decay

3 115) The symbols H and H represent 1 1

A) isotopesB) alpha particles

C) electronsD) deuterium ions

16) Which equation represents nuclear fission?226 222 4A) Ra ‡‡ˆ Rn + He 88 86 29 4 12 1B) Be + He ‡‡ˆ C + n4 2 6 0235 1 141 92 1C) U + n ‡‡ˆ Ba + Kr + 3 n + Q 92 0 56 36 024 24 0D) Na ‡‡ˆ Mg + e11 12 -1

17) After the decay of a radioactive sample, helium gas was oneof the products. This suggests that the nucleardisintegrations consisted ofA) positron emissionsB) beta decays

C) alpha decaysD) gamma emissions

18) Which equation is a step in the Uranium DisintegrationSeries?

234 230 4A) Th ‡‡ˆ Ra + He 90 88 2

234 234 0B) Th ‡‡ˆ Pa + e 90 91 -1

234 226 0C) Th ‡‡ˆ Ac + e 90 89 -1

234 226 4D) Th ‡‡ˆ Ra + He 90 88 2

13119) I initially decays by emission of beta particles. Beta 53particles are

A) electromagnetic wavesB) neutrons

C) electronsD) protons

20) The function of the moderator in a nuclear reactor is toA) produce extra neutronsB) speed up neutronsC) slow down neutronsD) absorb neutrons

21421) Which is an isotope of X? 83

210A) X 82

214B) X 84

214C) X 82

210D) X 83

23822) In the Uranium Disintegration Series, when an atom of U 92 206decays to Pb, the total number of beta particles emitted is 82

A) 2 B) 14 C) 6 D) 8

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23) Which isotope is used in defining the atomic mass unit?12A) C 6

16B) O 8

1C) H1

238D) U 92

4424) Which is an isotope of Sc? 21

44A) Ca20

46B) Sc21

44C) Ti22

46D) Ca20

25) Which two symbols represent isotopes of the sameelement?

6 8A) X and X2 2

2 4B) X and X2 4

8 8C) X and X2 4

3 2D) X and X2 3


A pure sample of radon (Rn) gas is sealed inside a glass tube. Thehalf-life of radon is 4 days.

26) The contents of the tube were analyzed after twenty daysand another gas was found in addition to the radon. Thenew gas is most likelyA) heliumB) oxygen

C) hydrogenD) nitrogen

27) If the pressure inside the tube were decreased to one-half,the half-life of the radon would beA) decreased to one-quarterB) unchangedC) decreased to one-halfD) doubled

28) Which nucleus has the greatest nuclear charge?4A) Z2

7B) Y3

8C) X5

2D) W1

27 4 30 129) The equation Al + He ‡‡ˆ P + n is an example of 13 2 15 0

A) beta decayB) alpha decay

C) natural transmutationD) artificial transmutation

30) The splitting apart of a heavier nucleus to form lighter nucleiis calledA) beta emissionB) positron emission

C) fusionD) fission

31) A certain radioactive isotope with a half-life of 5.0 minutesdecays to a stable (nonradioactive) nucleus by emitting onealpha particle.

The difference between the atomic number of the originalnucleus and the atomic number of the new stable nucleus isA) 4 B) 3 C) 1 D) 2

32) Given: Mass of a proton == 1.007277 amu Mass of a neutron == 1.008665 amu Mass of an electron == 0.0005486 amu 4 Mass of a He nucleus == 4.001509 amu 2

4 What is the mass defect of a He nucleus? 2

A) 0.029278 amu B) 1.985018 amu C) 1.985567 amu D) 0.030375 amu


238An atom of U absorbs a neutron as indicated in the equation 92238 1 U + n ‡‡ˆ Y. 92 0

23833) How many neutrons does U have in its nucleus? 92

A) 238 B) 237 C) 146 D) 147

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34) The atomic number of the element Y isA) 91 B) 92 C) 89 D) 90

35) Which device is used to produce a stream of high-velocitycharged particles?A) photographic platesB) cyclotronC) electroscopeD) Geiger counter

36) Isotopes of the same element must have differentA) mass numbersB) numbers of electronsC) atomic numberD) numbers of protons

37) Which device is used to detect nuclear radiation?A) cyclotronB) linear accelerator

C) cloud chamberD) synchrotron

838) The total number of nucleons in an atom of B is 5

A) 5 B) 13 C) 8 D) 3

39) When a nucleus captures an electron, the mass number ofthe nucleusA) increasesB) decreasesC) remains the same

40) A lithium nucleus contains three protons and four neutrons.What is its atomic mass number?A) 4 B) 3 C) 1 D) 7

41) Neutrons are used in some nuclear reactions as bombardingparticles because they areA) uncharged and have negligible massB) negatively charged and are attracted by the nucleusC) uncharged and are not repelled by the nucleusD) positively charged and are repelled by the nucleus

42) The diagram below represents an inverted test tube over asample of a radioactive material. Helium has collected in thetest tube.

The presence of helium indicates that the sample is mostprobably undergoing the process ofA) alpha decayB) gamma emission

C) beta decayD) neutron decay

43) What kind of nuclear reaction is represented by theequation below?

14 4 17 1 N + He ‡‡ˆ O + H 7 2 8 1

A) artificial transmutationB) nuclear fissionC) alpha decayD) beta decay

218 21444) In the nuclear reaction Po ‡‡ˆ Pb + X, the X represents 84 82

1A) n0

0B) e+1

4C) He2

0D) e-1

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45) The fission process in a nuclear reactor is controlled byregulating the number of availableA) positronsB) protons

C) electronsD) neutrons

46) Which device is normally used to accelerate chargedparticles?A) electroscopeB) Geiger counter

C) cyclotronD) cloud chamber

47) Which part of a nuclear reactor would most likely containplutonium?A) control rodB) fuel rod

C) shieldingD) moderator

2 1 148) In the reaction Q + H ‡‡ˆ H + n, Q represents the energy 1 1 0needed to separate the neutrons from the deuterium nucleus.

�2 ’Given: Mass of deuterium | H| = 2.0141 amu ‘1 “ �1 ’ Mass of hydrogen | H| = 1.0078 amu ‘1 “ �1 ’ Mass of neutron | n| = 1.0087 amu ‘0 “

What is the value of Q?

A) 4.0306 amu B) 2.0165 amu C) 0.0024 amu D) 0.0009 amu

449) How many nucleons are in a He nucleus? 2

A) 8 B) 6 C) 4 D) 2

50) Which device is used to accelerate a charged particle?A) a cloud chamberB) a cyclotronC) an electroscopeD) a photographic plate

51) What is the energy equivalent of a mass of 1 kilogram?

A) 9 x 107 JB) 9 x 1010 J

C) 9 x 1016 JD) 9 x 1013 J

52) Which graph best represents the relationship betweenenergy and mass in the mass-energy equation?

A)

B)

C)

D)

23853) An atom of U absorbs a neutron as indicated in the equation 92238 1 U + n ‡‡ˆ Y. 92 0

238If the U atom decays before the neutron can be absorbed, 92then according to the Uranium Disintegration Series, the238 U atom will emit 92

A) a neutron B) an alpha particle C) a beta particle D) a positron

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131 13154) I initially decays by emission of beta particles. When I 53 53decays by beta emission, it becomes

130A) I 53

135B) Xe 54

131C) Xe54

129D) Sb 51

55) The function of a moderator in a nuclear reaction is toA) slow down neutronsB) absorb neutronsC) speed up neutronsD) produce more neutrons

56) If a certain radioactive isotope has a half-life of 2 days, howmuch of a 64-kilogram sample of the isotope will remain after10 days?A) 1 kgB) 4 kg

C) 2 kgD) 32 kg

57) Which equation represents a part of the UraniumDisintegration Series?

3 1 4A) H + H ‡‡ˆ He + energy1 1 2230 214 4 B) Th ‡‡ˆ Pb + x He 90 82 2 235 1 90 140 1C) U + n ‡‡ˆ Sr + Xe + 6 n 92 0 38 54 014 4 17 D) N + He ‡‡ˆ O + y 7 2 8

58) How much energy is released when 1 x 10-3 kilogram ofmatter is converted to energy?

A) 9 x 1013 JB) 9 x 1016 J

C) 3 x 108 JD) 3 x 105 J

59) How many beta particles are given off when one atom ofU-238 completely disintegrates to Pb-206?A) 8B) 6

C) 14D) 10

60) What is the force which holds the nucleons of an atomtogether?A) atomic forceB) nuclear force

C) magnetic forceD) coulomb force

230 214 4 61) In the equation, Th ‡‡ˆ Pb + x He, what is the number of 90 82 24 He particles represented by the coefficient x?2

A) 1 B) 3 C) 4 D) 2

24 2462) In the reaction Na ‡‡ˆ Mg + x, what does x represent? 11 12

A) an alpha particle B) a beta particle C) a positron D) a neutron

63) Which group of particles can all be accelerated by acyclotron?A) neutrons, protons, and alpha particlesB) electrons, neutrons, and protonsC) alpha particles, electrons, and neutronsD) protons, alpha particles, and electrons

14 4 1764) In the equation, N + He ‡‡ˆ O + y, y represents 7 2 8

A) an alpha particle B) an electron C) a neutron D) a proton

65) What is the mass number of an atom with 9 protons,11 neutrons, and 9 electrons?A) 29B) 20

C) 18D) 9

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physics week 16(sem. 2) - st. francis preparatory schoolenergy per nucleon versus nucleon number...

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