226
6 Appendices
some skepticism. This issue is discussed further in Sect. 2.2, where it is pointed out
that, despite this complication, a diffusion model predicts critical masses in good
accord with experimentally-measured values.
6.8 Appendix H: Exercises and Answers
1.1 Compute Q-values for the following reactions. Reaction (a) produces highenergy neutrons for use in so-called “boosted” fission weapons. Reaction
(b) is important in the production of tritium for use in reaction (a). Reaction (c) is a hypothetical fission reaction. Reaction (d) is an example of how
alpha-bombardment of a light element can release neutrons, an important
consideration in avoiding pre-detonation in fission weapons.
(a)
2
1 H +
3
1 H →
4
2 He +
1
0 n
(b)
6
3 Li +
1
0 n →
3
1 H +
4
2 He
(c)
1
0 n +
238
92 U → 2
118
46 Pd
+ 3
1
0 n
(d)
4
2 He +
27
13 Al →
30
15 P +
1
0 n
1.2 To melt one gram of ice at 0 C into 1 g of water at 0 C requires input of 80
physical calories of heat energy. If all of the energy involved in the alpha-decay
of one gram
226 Ra over the course of one day could directed into melting ice,
how many grams of ice could be melted per day? The decay rate of
226 Ra is 3.7
× 10
10 per gram per second, and the alphas have kinetic energies of 4.8 MeV.
1.3 Prove Eq. (1.20) (assume classical mechanics), and then apply it to the case
of radium decay discussed in Sect. 1.2. What will be the kinetic energy of the
emergent α-particle? How does your result compare to the value of 4.78 MeV
quoted in the Chart of the Nuclides?
1.4 For each of the reactions below, compute the energy of the resulting γ -ray,
assuming that it is moving forward after the reaction. Assume that the target
nucleus is stationary in each case.
(a)
1
1 H +
16
8 O →
17
9 F + γ (K H = 4.9 MeV)
(b)
4
2 He +
27
13 Al →
31
15 P + γ (K He = 6.5 MeV)
(c)
56
26 Fe +
94
40 Zr →
150
66 Dy + γ (K Fe = 50 MeV)
1.5 For each of the two-body reactions below, compute the Q-value of the reaction,
the threshold energy (if any), and the kinetic energies and directions of motion
of the products. Assume that the target nucleus is initially stationary in each
case.
(a)
4
2 He +
27
13 Al →
30
15 P +
1
0 n (K He = 5 MeV)
(b)
2
1 H +
3
1 H →
4
2 He +
1
0 n (K H = 3 MeV)
(c)
4
2 He +
19
9 F →
22
10 Ne +
1
1 H (K He = 2.75 MeV)
(d)
4
2 He +
56
26 Fe →
35
16 S +
25
12 Mg (K He = 30 MeV)
(e)
16
8 O +
238
92 U →
252
99 Es +
2
1 H (K O = 60 MeV)
6 Appendices
some skepticism. This issue is discussed further in Sect. 2.2, where it is pointed out
that, despite this complication, a diffusion model predicts critical masses in good
accord with experimentally-measured values.
6.8 Appendix H: Exercises and Answers
1.1 Compute Q-values for the following reactions. Reaction (a) produces highenergy neutrons for use in so-called “boosted” fission weapons. Reaction
(b) is important in the production of tritium for use in reaction (a). Reaction (c) is a hypothetical fission reaction. Reaction (d) is an example of how
alpha-bombardment of a light element can release neutrons, an important
consideration in avoiding pre-detonation in fission weapons.
(a)
2
1 H +
3
1 H →
4
2 He +
1
0 n
(b)
6
3 Li +
1
0 n →
3
1 H +
4
2 He
(c)
1
0 n +
238
92 U → 2
118
46 Pd
+ 3
1
0 n
(d)
4
2 He +
27
13 Al →
30
15 P +
1
0 n
1.2 To melt one gram of ice at 0 C into 1 g of water at 0 C requires input of 80
physical calories of heat energy. If all of the energy involved in the alpha-decay
of one gram
226 Ra over the course of one day could directed into melting ice,
how many grams of ice could be melted per day? The decay rate of
226 Ra is 3.7
× 10
10 per gram per second, and the alphas have kinetic energies of 4.8 MeV.
1.3 Prove Eq. (1.20) (assume classical mechanics), and then apply it to the case
of radium decay discussed in Sect. 1.2. What will be the kinetic energy of the
emergent α-particle? How does your result compare to the value of 4.78 MeV
quoted in the Chart of the Nuclides?
1.4 For each of the reactions below, compute the energy of the resulting γ -ray,
assuming that it is moving forward after the reaction. Assume that the target
nucleus is stationary in each case.
(a)
1
1 H +
16
8 O →
17
9 F + γ (K H = 4.9 MeV)
(b)
4
2 He +
27
13 Al →
31
15 P + γ (K He = 6.5 MeV)
(c)
56
26 Fe +
94
40 Zr →
150
66 Dy + γ (K Fe = 50 MeV)
1.5 For each of the two-body reactions below, compute the Q-value of the reaction,
the threshold energy (if any), and the kinetic energies and directions of motion
of the products. Assume that the target nucleus is initially stationary in each
case.
(a)
4
2 He +
27
13 Al →
30
15 P +
1
0 n (K He = 5 MeV)
(b)
2
1 H +
3
1 H →
4
2 He +
1
0 n (K H = 3 MeV)
(c)
4
2 He +
19
9 F →
22
10 Ne +
1
1 H (K He = 2.75 MeV)
(d)
4
2 He +
56
26 Fe →
35
16 S +
25
12 Mg (K He = 30 MeV)
(e)
16
8 O +
238
92 U →
252
99 Es +
2
1 H (K O = 60 MeV)