Answer
See answers.
Work Step by Step
a. This is named a "pick-up" reaction because helium-3 has picked up a neutron, at the expense of the carbon atom.
b. The reaction is
$$^{3}_{2}He + \;^{12}_{6}C\rightarrow\;X +\alpha$$
Conserve nucleon number: 3 + 12 = A + 4. We see that A = 11.
Conserve charge: 2 + 6 = Z + 2. We see that Z = 6.
The unknown product is Carbon-11.
$$^{3}_{2}He + \;^{12}_{6}C\rightarrow \;^{11}_{6}C +\alpha$$
c. Calculate the Q-value, using data from Appendix B. We use atomic masses.
$$Q=\left(m(^{3}_{2}He)+m(^{12}_{6}C)-m(^{11}_{6}C)-m_{\alpha} \right)c^2$$
$$ =\left(3.016029u+12.000000u-11.011434u-4.002603u\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$
$$=1.856MeV$$
The Q-value is positive. The reaction is exothermic.