Q$11$M$.9$ The potential energy function for a proton or neutron in an atomic nucleus can be crudely modeled as being a "box" that is about $4fm=4{10}^{-15}m$ wide. Imagine that we put $12$ neutrons $($which are fermions$)$ into such a box.

$($a$)$ Find the neutrons' minimum total energy in this case.

$($b$)$ How much lower would this minimum energy become if we changed one$-$half of the neutrons to protons?

made a transition of $n=-1.$

Problem $5.$ Q$11$M$\mathrm{.}9+(+)$ If one of the nucleons in $($b$)$ makes a transition from $n=4$ to $n=3,$ what will be the energy and wavelength of the emitted photon? How does this energy compare to the energy of a typical atomic transition? $[$Neutrons and protons each have spin $\frac{1}{2}.$