Answer
See answers.
Work Step by Step
a.
$$n + \;^{232}_{90}Th\rightarrow\;? +\gamma$$
Conserve nucleon number: 1 + 232 = A + 0. We see that A = 233.
Conserve charge: 0 + 90 = Z + 0. We see that Z = 90.
$$n + \;^{232}_{90}Th\rightarrow\;^{233}_{90}Th +\gamma$$
b.
$$n + \;^{137}_{56}Ba\rightarrow\;^{137}_{55}Cs\; +\;?$$
Conserve nucleon number: 1 + 137 =137 + A. We see that A = 1.
Conserve charge: 0 + 56 = 55 + Z. We see that Z = 1.
$$n + \;^{137}_{56}Ba\rightarrow\;^{137}_{55}Cs +\;^{1}_{1}H$$
An alternate answer is a proton.
c.
$$d + \;^{2}_{1}H\rightarrow\;^{4}_{2}He + \;?$$
Conserve nucleon number: 2 + 2 = 4 + A. We see that A = 1.
Conserve charge: 1 + 1 = 2 + Z. We see that Z = 0.
$$d + \;^{2}_{1}H\rightarrow\;^{4}_{2}He + \;\gamma$$
d.
$$\alpha + \;^{197}_{79}Au\rightarrow\;? + \;d$$
Conserve nucleon number: 4 + 197 = A + 2. We see that A = 199.
Conserve charge: 2 + 79 = Z + 1. We see that Z = 80.
$$\alpha + \;^{197}_{79}Au\rightarrow\;^{199}_{80}Hg + \;d$$
