Answer
See answers.
Work Step by Step
a. Calculate the binding energy using the masses of the components and the mass of the nucleus. See Appendix B.
$$E_{binding}=\left( 2m(^{4}_{2}He) -m(^{8}_{4}Be)\right)c^2$$
$$ =\left( 2(4.002603u) -(8.005305u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$
$$ =-0.092MeV$$
The binding energy is negative, which means that the nucleus is unstable.
b. Calculate the binding energy using the masses of the components and the mass of the nucleus. See Appendix B.
$$E_{binding}=\left( 3m(^{4}_{2}He) -m(^{12}_{6}C)\right)c^2$$
$$ =\left( 3(4.002603u) -(12.000000u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$
$$ =7.3MeV$$
The binding energy is positive, which means that the nucleus is stable.