Dr. Johnny B. Holmes

X-rays and Atomic Structure
Nuclear Physics
Nuclear Stability Data
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Outline
Supplementary Homework Problems
Answers to Problems
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OUTLINE

1. Energy and wavelengths S-66
1. E_photon = hf; fl = c; therefore, E = hc/l
2. E_edge » 13.6 eV (Z-1)²
2. Interference (x-ray diffraction)
1. n_max l = 2 d sin(q _max)
3. Absorption S-67
1. intensity (I) vs distance (x) and material (m ): I(x) = I_oe^{-m X}
2. intensity vs wavelength or Energy: m (l ) or m (E)
1. photoelectric effect: m_¯ (I_­ ) as E_g­ (l_g¯ )
2. Compton scattering: m_¯ (I_­ ) as E_g­ (l_g¯ )
3. pair production: m_­ (I_¯ ) as E_g­ (l_g¯ )

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66. Explain how an x-ray machine produces x-rays. This should include a discussion of discrete and continuous spectra.

67. What are the three main means of absorbing x-rays and for which energy range is each dominant?

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66. A beam of electrons is accelerated and then smashed against a target. The electrons lose energy in the collision which shows up as the continuous spectrum of x-rays (photons of different size depending on the energy lost by the electrons in the collision); and the electrons knock electrons out of the target atoms which then re-absorb electrons and then emit discrete x-rays based on the energy levels of the target atoms.

67. (a) photoelectric effect, dominant below 1 Mev; (b) Compton scattering, dominant between 1 Mev and 5 Mev; (c) pair production, dominant above 5 Mev.

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Outline
Supplementary Homework Problems
Answers to Problems
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1. Nuclear structure
1. atomic number
2. atomic mass
3. nuclear binding: nuclear force and nuclear energy
2. Radioactivity S-68 to 71
1. types
1. photons (gamma rays, g ): can't change q or m, accompanies other reactions
2. electrons (beta-, b ^-) and positrons (beta+ ,b ⁺): changes q but not m
3. alpha (a ) particles: changes both q and m
4. induced radioactivity ( ex. production of radioactive C¹⁴ in the atmosphere)
2. half-life: N _µ DN / Dt leads to N = N_oe^{-l t}
   so when N = (1/2)N_o then t = T_1/2 and e^-lT = 1/2 , or T_1/2 = ln(2) / l
3. activity: A = l N so A(t) = A_oe^{-l t}
4. absorption of each
3. Nuclear Power S-72 to 74
1. fission
1. the bomb
2. the reactor
1. power and fuel
2. decay products
3. breeder reactors
4. relative safety
2. fusion
1. the bomb
2. controlled fusion
1. magnetic confinement
2. inertial confinement
4. Biological effects S-75,76
1. units
2. background levels
3. recommended maximum levels
5. Sub-atomic particles - quarks!

68. Th²³⁴ decays by beta decay. What does it decay to? Write the "equation" for this reaction.

69. The stable isotopes of iron are ₂₆Fe⁵⁶ , ₂₆Fe⁵⁷ , and ₂₆Fe⁵⁸ . a) What type of decay would ₂₆Fe⁶¹ most likely undergo? b) What would it become? c) What type of decay would ₂₆Fe⁵² most likely undergo? d) Write the "equation" for this reaction. e) Would Fe⁶¹ or Fe⁵² also be likely to decay by electron capture?

70. a) What type of decay would C¹⁴ most likely undergo? b) What would the "equation" for this reaction be? c) What would the energy released in this decay be? (The mass of C¹⁴ is 14.003233 amu.)

71. The half life of C¹⁴ is 5730 years. a) What is the decay constant for C¹⁴ ? b) The ratio of C¹⁴ to C¹² in the atmosphere is 1.3x10^-12 . What is the present activity of a 12 gram sample of carbon taken from a "modern" bone? c) A 12 gram sample of carbon taken from a bone at an archeo- logical site has an activity of 35 counts per minute. Assuming that C¹⁴ was formed at the same rate then as it is now, how old is the bone?

72. a) What is a moderator in a nuclear reactor? b) What is it used? c) Explain why it is impossible for a nuclear reactor to blow up as a

nuclear bomb.

73. What is a breeder reactor?

74. Distinguish fusion from fission. Which do present reactors employ? Which do present nuclear weapons employ?

75. Distinguish between exposure dose, absorption dose, and activity; and know which units go with which doses.

76. Know what the approximate background level of radiation is, and know what the whole-body dose limits are for the general population.

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

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

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

71. a) 1.21 x 10^-4 /yr = 2.30 x 10^-10 /min; b) 179.4 counts/min; c) 13,510 yrs.

75. See the nuclear data sheet.

76. See the nuclear data sheet.

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