I have 2 questions regarding the solution to the following question:
The solution states that:
Mathematically, I understand how the end result
$$Q=BE\left({}^{A-4}_{Z-2}\mathrm{Y}\right)+BE\left({}^{4}_{2}\mathrm{He}\right)-BE\left({}^{A}_{Z}\mathrm{X}\right)$$ was obtained.
This is because from the definition of nuclear mass the second equality is splitting each of the 3 species into 3 terms, where the first is $$m_N\left({}^{A}_{Z}\mathrm{X}\right)=Zm_p +(A-Z)m_N - BE\left({}^{A}_{Z}\mathrm{X}\right)$$ and the similarly for the 2 other species by virtue of the formula for nuclear mass given below:
My 2 questions are:
- $Q$ has dimensions of energy, so why are the masses not being multiplied by $c^2$, ie. $$Q=m_N\left({}^{A}_{Z}\mathrm{X}\right)c^2-m_N\left({}^{A-4}_{Z-2}\mathrm{Y}\right)c^2-m_N\left({}^{4}_{2}\mathrm{He}\right)c^2\,?$$
- In the algebra that follows $m_N$ is being used, but this is the mass of the nucleus, should it not be $m_n$ (mass of neutron)? I don't see how $m_N$ can possibly be justified here since the proton mass has already been accounted for with $m_p$. Is this a typo, or something I am not understanding correctly?
I have read this similar question and I own a copy of the Williams textbook but neither answer my question here.