RADIOACTIVITY

Dr. Holmes

Nuclear Physics
Nuclear Applications
Particle Physics
Nuclear Stability
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Outline
Study Questions
Supplementary Homework Problems
Answers to Problems

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1. Nuclear Structure [Q-1; S-78]
1. size of nucleus
2. structure of nucleus
3. the nucleus
1. charge - elements (Z º number of protons in nucleus)
2. mass - isotopes (A º Z + N where N º number of neutrons)
3. stability
4. radiations (from the nucleus, not the electronic shells)
5. mass defect and binding energy (D m = {[Z· m_H + N· m_n] - m_atom}, BE = Dm· c²)
2. Radioactivity
1. rate of decay (dN/dt µ N) [S-79,80]
1. exponential decay (N = N_oe^-l t)
2. decay constant (l )
3. half life (T_1/2 = ln[2]/l )
2. activity [Q-2 to 6; S-81 to 86]
1. exponential decay (A º -dN/dt = A_oe^-l t)
2. units (Bq., Curie) (see nuclear data sheet)
3. types of decay
1. alpha (a )
2. beta (b ^-)
3. others (b ⁺ = positron, g = gamma, p, n, E.C., I.C.)
4. reaction formulas
5. "missing" particle: the neutrino (_on^o)
4. radioactive series [Q-7]
1. U²³⁸ (4N+2) T_1/2 = 4.51x10⁹ years, goes to Pb²⁰⁶
2. U²³⁵ (4N+3) T_1/2 = 7.12x10⁸ years, goes to Pb²⁰⁷
3. Th²³² (4N) T_1/2 = 1.39x10¹⁰ years, goes to Pb²⁰⁸
4. Np²³⁷ (4N+1) T_1/2 = 2.20x10⁶ years, goes to Bi²⁰⁹
5. man-made and other radioactive elements [Q-8; S-87]
3. X-rays (Supplement)
1. x-ray photons [Q-9]
2. x-ray machines Q-10; [S-88]
3. mechanism of x-ray production [Q-11,12,13]
1. continuous radiation (hf_max = eV, l _min = c/f_max)
2. characteristic radiation (atomic: due to inner e^-, E_{to ionize} = 13.6 eV (Z-1)² )
4. nuclear x-rays (NOT due to electronic shells)
5. absorption of x-rays [Q-14; S-89]

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STUDY QUESTIONS:
1) Why does ₉₂U²³⁸ have a higher ratio of neutrons/nucleons than ₆C¹² ?

2) Describe the three major types of radiation emitted by radioactive elements.

3) What is a neutrino and in what type of process it is emitted?

4) What is K-electron capture and what type of radiation results?

5) Describe Internal Conversion (I.C.) .

6) Tell how the atomic number, neutron number, and mass number change for alpha decay, beta decay, positron emission, and K-capture.

7) Be able to follow one path along one radioactive series. You do not have to follow all branch points, but you should indicate where the atom has a choice (that is, a branch point).

8) How are man-made or artificial radioisotopes produced?

9) What are x-rays?

10) Tell how an x-ray machine produces x-rays.

11) Why is there a minimum wavelength for the x-rays produced in an x-ray tube?

12) Briefly describe the mechanism of x-ray production. Your description should include some words about continuous and characteristic radiation.

13) Tell how K-series radiation is produced. What is the difference between Ka and Kb radiation? How does L-series radiation differ from K-series?

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SUPPLEMENTARY PROBLEMS (S- ):
78) a) What is the binding energy of ₈O¹⁶ (mass = 15.994915 amu)? b) What is the binding energy per nucleon for ₈O¹⁶ ?

79) The half life of Th²³² is 13.9 billion years. The age of the earth is 4.6 billion years. What percentage of a pocket of originally pure Thorium is still Thorium now?

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ANSWERS TO SUPPLEMENTARY PROBLEMS:
78) a) 127.55 MeV b) 7.97 MeV/nucleon.

79) 78% .

80) a) 1.21 x 10^-4 /yr = 2.30 x 10^-10 /min; b) 59.8 counts/min; c) 17,740 yrs.

81) a) one gram by definition; b) 3 metric tons (3000 kg).

82) a) ₉₀Th²³⁴ ; b) 234.0436 amu.

83) a) 6.2x10^-14 meters; b) 7.44X10^-15 meters; c) answer to a is greater than the answer to b by factor of 8.3 which indicates quantum mechanical tunnelling has occurred.

84) ₉₁Pa²³⁴ ; ₉₀Th²³⁴ goes to ₉₁Pa²³⁴ +_-1b ⁰ + antineutrino + gamma.

85) a) b ; b) ₂₇Co⁶¹; c) positron (b ⁺ ); d) ₂₆Fe⁵² goes to ₂₅Mn⁵² + ₊₁b ⁰ + neutrino; e) ₂₆Fe⁵² .

86) a) b ; b) ₆C¹⁴ goes to ₇N¹⁴+ _-1b ⁰ + antinuetrino; c) 0.148 MeV.

e) E = 7436 eV, l = 0.167 nm .

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Outline
Study Questions
Supplementary Homework Problems
Answers to Problems

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1. Radiation Units and Doses
1. absorption of radiation [Q-15,16]
1. alpha
2. beta
3. gamma
1. photoelectric effect
2. compton scattering
3. pair production
4. total
4. units (Roentgen)
5. detectors
1. cloud and bubble chambers
2. geiger counters
3. scintillation counters
2. radiation damage [Q-17,18,19]
1. structural
2. biological
3. units (rad, rem)
2. Nuclear Energy
1. cross sections (Probability: P_f = s _f/[s _f+s _abs+s _esc] ) [Q-20]
2. chain reactions (k º N_avg P ) [Q- 21]
3. reactor criticality Q-22
4. moderators (slow neutrons down since P_f(slow) > P_f(fast) ) [Q-23]
5. power reactors [Q-24 to 27]
1. fuels
2. types
1. boiling water reactors
2. gas-cooled reactors
3. breeder reactors
3. safety
6. fusion [Q-28,29; S-90,91]
1. fuels
2. high temperature confinement problems
1. gravitational: the sun's method
2. magnetic
3. inertial
3. safety

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STUDY QUESTIONS:
15) Compare the penetrating abilities of alpha particles, beta particles, and gamma rays. To what are the differences attributed?

16) What are the three mechanisms of x-ray absorption? For what energy range is each the dominant mechanism?

17) If the skin and clothing provide adequate shielding for our vital organs from beta and alpha particles, why are alpha and beta emitters considered dangerous?

18) Although not completely understood, what is the mechanism of tissue destruction by ionizing radiation?

19) Know the definitions of Roengen, rad, rem, and Curie and which are for exposure, absorption, and activity.

20) What is meant by "cross-section" in connection with nuclear reactions?

21) Tell what is meant by a chain reaction.

22) What do the words subcritical, critical, and supercritical mean in connection with nuclear fission?

23) What is a moderator, and why is it used? What are the characteristics of a good moderator?

24) How are controlled nuclear reactors controlled?

25) What is poisoning in the case of fuel elements for a fission reactor?

26) What is a breeder reactor?

27) What makes a boiling water reactor inherently stable and thus contributes to its safety?

28) What is the result of the Carbon cycle? How much energy in Joules would be released if the hydrogen in 18 grams of water went through the carbon cycle?

29) Give some advantages of fusion reactions over fission reactions as sources of power.

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SUPPLEMENTARY PROBLEMS (S- ):
90) a) What is the energy from fissioning one gram of ₉₂U²³⁵ if the average energy per fission is 200 MeV ? b) What is the energy for fusing one gram of ₁H¹ into ₂He⁴ if the average energy per fusion is 26.7 MeV ?

91) The energy received from the sun at the top of the earth's atmosphere is 1.35 kilowatts per square meter (assuming the sunlight is normal to the collector and the collector's efficiency is 100%). a) What is the total power output of the sun (the radius of the earth's orbit around the sun is 1.49x10⁸ km) ? b) How many metric tons (1000 kg = 1 metric ton) of hydrogen are "burned" each second by the sun? (Note: the sun's mass is 2x10³⁰ kg, so it has a lot of fuel. At this rate, it will take 10 billion years to burn up the fuel in the sun's core. When this happens the sun will become a red giant and fry the earth. The sun has been burning for about 4.6 billion years, so it has about 5.4 billion years left.)

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ANSWERS TO SUPPLEMENTARY PROBLEMS:
90) a) 8.17x10¹⁰ Joules; b) 6.4x10¹¹ Joules.

91) a) 3.77x10²⁶ Watts; b) 5.88x10⁸ tons/sec.

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(Extra topic - no study questions, no supplementary problems)

1. sub-atomic particles
2. bosons and fermions
3. strong and weak nuclear forces
4. leptons (6) - weak nuclear forces only
5. quarks (6) and baryons
1. hadrons (3 quarks)
2. mesons (2 quarks)
6. gluons - strong nuclear force
7. field quanta: photons, pions, others

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Nuclear Stability Table (first elements)
Nuclear Stability Table (selected elements)
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