Nucleon in Inifinte Square Well

[atomicpedals]

Homework Statement

Assuming an infinite square well of radius 2.8E-13cm, find the normalized wave functions and the energies of the four lowest states for a nucleon.

2. The attempt at a solution

I want to say that the wave function is $\psi (x) = \sqrt{\frac{2}{a}} sin(\frac{n \pi}{a} x)$. Which then leads to possible energies of $E_{n}=\frac{n^{2} \pi^{2} \hbar^{2}}{2 m a^{2}}$. Where in this case $a = 2(2.8 \times 10^{-13}) = 5.6 \times 10^{-13}$. And m would be the nucleon mass. Does this work?

 

[atomicpedals]

I think I've convinced myself this is valid; or at least not totally off base.