Chapter 45

Fission and Fusion

Multiple Choice

1. A beam of 1-MeV gamma rays incident on a piece of 1/2-cm thick lead is reduced by 50% of its initial value. How thick must the lead be to reduce the beam to 1% of its initial value?

a. 1.1 cm b. 2.2 cm c. 3.3 cm d. 4.4 cm e. 8.4 cm

2. A neutron is known to undergo beta decay (n → p + e– + ν ). A reasonable mean lifetime for free neutrons is

a. 10 years b. 10 hours c. 10 days d. 10 minutes e. 10–23 s

3. A neutron is characterized by the term “thermal neutron” when

a. its energy is of the order kT, where T is on the order of 0°C. b. its energy is of the order kT, where T is on the order of 0 K. c. its energy is of the order kT, where T is on the order of 273 K. d. its energy is of the order kT, where T is on the order of 100°C. e. its energy is of the order kT, where T is on the order of 0°R.

4. A thermal neutron has an energy (in eV) on the order of

a. 40 b. 0.4 c. 4 d. 0.04 e. 400

5. The nuclear scattering cross-sections of neutrons depend most strongly on the neutron’s

a. mass b. area c. volume d. speed e. charge

389

390 CHAPTER 45

6. Find the number of nuclei per unit volume (n = nuclei/cm3) for lead.

atomic weight = 202.7 density = 11.5 g/cm3 Avogadro’s number = 6.02 × 1023

a. 2.5 × 1022 b. 3.4 × 1022 c. 2.9 × 1022 d. 2.9 × 1023 e. 2.0 × 1021

7. Find the unknown atomic number and mass number respectively, for the following reaction

n + U → X + 9438 Sr + 2n 235

92AZ

23592

14156

9236

23592

14156

9236

a. 141, 53 b. 140, 54 c. 53, 41 d. 54, 140 e. 54, 141

8. How much energy (in MeV) is released when a U fissions to Ba and Kr in the reaction

n + U → Ba + Kr + 3n?

m(n) = 1.008665 u m(U) = 235.043915 u m(Ba) = 140.9139 u m(Kr) = 91.8973 u u = 1.66 × 10–27 kg

a. 100 b. 50 c. 200 d. 150 e. 250

Fission and Fusion 391

9. Approximately how much uranium (in kg) must undergo fission per day to provide 1000 MW of power? (Assume an efficiency of 30%). The nuclear reaction is

n + U → Ba + Kr + 3n 23592

14156

9236

m(n) = 1.008665 u m(U) = 235.043915 u m(Ba) = 140.9139 u m(Kr) = 91.8973 u u = 1.66 × 10–27 kg

a. 1.0 b. 3.5 c. 2.3 d. 4.6 e. 0.1

10. A self-sustained chain reaction occurs when the reproduction constant, K, is equal to

a. 3.0 b. 2.0 c. 2.5 d. 1.0 e. 0.5

11. What is the average kinetic energy (in keV) of an ion that has a temperature of 108 K?

a. 8 b. 13 c. 4 d. 16 e. 21

12. Approximately how fast is an ion of helium moving if it is in a plasma with a temperature of 108 K? m(He) = 4.002603 u and u = 1.66 × 10–27 kg.

a. 106 m/s b. 104 m/s c. 102 m/s d. 10 m/s e. 1 m/s

13. What energy is needed (in MeV) so two deuterium atoms moving together will reach the necessary 10–14 m for fusion?

a. 0.511 b. 0.14 c. 2.5 d. 4.3 e. 1.0

392 CHAPTER 45

14. How fast must two deuterium atoms be moving so they can overcome the Coulomb force of repulsion, and attain the necessary 10–14 m for fusion? (m( H) = 2.0141 u) 2

1

a. 3.9 × 106 m/s b. 1.3 × 106 m/s c. 2.6 × 106 m/s d. 5.2 × 106 m/s e. 3.7 × 106 m/s

15. A principal mechanism for energy loss during nuclear fusion is bremsstrahlung. This loss is associated with

a. x-rays emitted due to electron-ion collisions. b. radiation losses due to T4 losses. c. conduction losses associated with ΔT. d. convection losses associated with ΔT. e. neutron collisions with atoms of moderator.

16. Calculate the half-value thickness (in mm) of lead if it reduces the intensity of a beam of x-rays whose wavelength is 10 pm by a factor of two. (The linear absorption coefficient of lead is 43 cm–1 for x-rays of wavelength 60 × 10–12 m).

a. 0.24 b. 0.20 c. 0.12 d. 0.16 e. 0.18

17. One roentgen is defined as

a. the amount of ionizing radiation that will produce 1/3 × 10–9 C of electric charge in 1 cm3 of air under standard conditions.

b. the amount of radiation that deposits 10–2 J of energy into 1 kg of absorbing material.

c. the amount of radiation needed for ionization of an atom. d. the amount of radiation needed for dissociation of a molecule. e. the amount of radiation that deposits 1 erg of energy in 1 g of air.

18. One rad is

a. the amount of radiation that deposits 10–2 J of energy into 1 kg of absorbing material.

b. the amount of ionizing radiation that will produce 1/3 × 10–9 C of electric charge in 1 cm3 of air under standard conditions.

c. the amount of radiation needed for ionization of an atom. d. the amount of radiation needed for dissociation of a molecule. e. the amount of radiation that deposits one erg of energy in 1g of material.

Fission and Fusion 393

19. A rem (roentgen equivalent in man) is defined as (the product of)

a. the dose in RBE. b. the dose in roentgen and the RBE factor. c. the dose in rad times the dose in roentgen. d. the dose in rad and the RBE factor. e. the dose in rad and energy of radiation.

20. Which of the following is not a radiation detector?

a. cloud chamber b. Geiger counter c. scintillation counter d. neutron activation e. spark chamber

21. When a fast neutron collides with a hydrogen or deuterium nucleus, the most likely result is that

a. the neutron has an appreciable gain in kinetic energy, the gain being greatest for head-on collisions.

b. the neutron has an appreciable gain in kinetic energy, the gain being greatest for oblique collisions.

c. the neutron has an appreciable loss in kinetic energy, the loss being greatest for head-on collisions.

d. the neutron has an appreciable loss in kinetic energy, the loss being greatest for oblique collisions.

e. the neutron is absorbed by the hydrogen or deuterium nucleus.

22. In order to control a nuclear reactor, control rods can be pulled out of or pushed into the reactor core by remote control. These rods control the reactor by

a. slowing down the fast neutrons so the neutrons can be absorbed by 238U. b. speeding up slow neutrons so the neutrons can be absorbed by 238U. c. slowing down fast neutrons so they cannot initiate further fusion reactions

in 235U. d. speeding up fast neutrons so they cannot initiate further fusion reactions in

235U. e. capturing thermal neutrons so they cannot initiate further fission reactions

in 235U.

23. Radiant energy reaching the Earth from the sun is not sufficient to keep the Earth’s surface temperature comfortable for life. The most likely source of the additional thermal energy is from

a. fusion of hydrogen nuclei in the Earth’s core. b. fusion of high Z nuclei in the Earth’s core. c. fission of radioactive nuclei inside the Earth. d. fission of radioactive nuclei in cosmic rays. e. deflection of radioactive nuclei in cosmic rays.

394 CHAPTER 45

24. Background radiation from cosmic rays and radoactive nuclei in our surroundings is about 0.13 rem/year. Suppose we assume this all comes from cosmic rays which have an RBE factor of 1.0. The RBE factor for the most dangerous types of radiation is 20. How many rads of the most dangerous radiation could a 100-year-old person have been exposed to in her lifetime without having gone over the recommended limit of 0.5 rem/year?

a. 0.37 b. 0.50 c. 1.85 d. 13 e. 37

25. The reaction 01 n is known as a _____ reaction. *1XX A

ZAZ

+→+

1 2

1m 2

a. beta capture b. beta emission c. neutron capture d. neutron emission e. photon emission

26. Radioactive technetium, a gamma emitter, is taken up by the heart muscle in a medical test. The detector for the radiation emitted from the heart could be a

a. Tokamak. b. quarter-wavelength antenna. c. Geiger counter. d. photoelectric tube. e. diffraction grating.

27. When a nucleus at rest spontaneously splits into fragments of mass m and m , the ratio of the momentum of to the momentum of m is

a. 21 mm +

1m− .

21 mm +− 2m

1−

b. .

c. .

d. 1

21

mmm +

+ .

e. 2

21

mmm +

+ .

Fission and Fusion 395

28. When a nucleus at rest spontaneously splits into fragments of mass and , the ratio of the velocity of to the velocity of is

1m 2m

1m 2m

a. 2

1

mm

− .

b. 1

2

mm

− .

c. . 1−

d. 21

1

mmm+

+ .

e. 21

2

mmm+

+ .

29. A radioactive sample with decay rate R and decay energy Q has power output

a. R

Q2

.

b. . RQ

c. . RQ2

0I=

d. equal to any of the above. e. equal to (a) or (c) above.

30. When a beam of nuclear radiation of initial intensity passes through a thickness x of material, the intensity of the beam exiting the material is I

a. . xeI μ−0

b. . xeI μ0

( )10 −− xeI μc. .

( )1−xμd. . 0 eI

( )xe μ−−I 1e. . 0

31. In neutron capture by an atomic nucleus, the atomic number changes by

−2 . a. b. −1 . c. 0.

+1 . d. +2 . e.

32. In neutron capture by an atomic nucleus, the mass number of the nucleus changes by

a. −2 . b. −1 . c. 0. d. +1 . e. +2 .

396 CHAPTER 45

33. Leda says that elements below 2656 Fe in mass number do not decay because the

nucleons in 2656 Fe have the greatest binding energy per nucleon. Denise says that

naturally occurring elements with mass numbers greater than that of 2656 Fe were

all created by fusion reactions in supernovae. Which one, if either, is correct, and why?

a. Denise, because there are no radioactive elements with Z < 26 . b. Leda, because we can create high Z nuclei with accelerators. c. Both, because some low Z elements decay, and high Z elements are created

in supernova explosions. d. Neither, because some low Z elements decay, and high Z elements are

created in supernova explosions. e. Neither, because no low Z isotopes decay, and only elements with Z < 26

are created in supernova explosions.

34. A nuclear reactor is said to be critical when the average number of neutrons from each fission event that cause(s) another fission event is

a. <1. b. 1. c. >1. d. any of the above. e. only (b) or (c) above.

35. The nuclear reaction(s) that is(are) most likely to be employed in fusion reactors on Earth is(are)

12 H + 1

2 H→23 He+ 0

1 n . a.

12 H + 1

2 H→13 H + 1

1 H . b.

c. 12 H + 1

3 H→24 He+ 0

1 n . d. all of the above. e. only (a) and (b) above.

Fission and Fusion 397

Open-Ended Problems

36. How much kinetic energy must a deuterium ion (charge 1.6 × 10–19 C) have to approach to within 10–14 m of another deuterium ion? (1 MeV = 1.6 × 10–13 J)

37. A beam of high-energy α-particles is incident upon a person and deposits 0.35 J of energy in 0.8 kg of tissue. What dose in rads and what equivalent dose in rems does the individual receive? [RBE α = 20]

38. The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing these elements into space. If we assume that at the time of the explosion there were equal amount of U-235 and U-238, how long ago did the star(s) explode that released the elements that formed our Earth? The present U-235/U-238 ratio is 0.007. [The half-lives of U-235 and U-238 are 0.7 × 109 yr and 4.47 × 109 yr.]

39. How many grams of U-235 must be fissioned every day to produce 1000 MW of electricity in a nuclear power plant that is 1/3 efficient? [Assume 208 MeV/fission and 1 MeV = 1.6 × 10–13 J]

40. How many grams of deuterium (atomic mass = 2.0141 u) must be fused to helium (atomic mass 4.0026 u) in one second to produce 3000 MJ of energy? [1 u = 1.66 × 10–27 kg]

398 CHAPTER 45

Fission and Fusion 399

Chapter 45

Fission and Fusion

1. c

2. d

3. a

4. d

5. d

6. b

7. d

8. c

9. b

10. d

11. b

12. a

13. b

14. c

15. a

16. d

17. a

18. a

19. d

20. d

21. c

22. e

23. c

24. c

25. c

26. c

27. c

28. b

29. b

30. a

31. c

32. d

33. c

34. e

35. d

36. 140 keV

37. 43.8 rad, 876 rem

38. 5.9 billion years

39. 3050 grams

40. 0.0053 grams

400 CHAPTER 45