This problem illustrates a simple, but reasonable, model of the atomic nucleus.

The diameter of the atomic nucleus is about $10$ fm $.$ A simple model of the nucleus is that protons and neutrons are confined in a one dimensional box of length $\backslash ($ L$=10\backslash )$ fm$.$ Consider a proton in such a box.

What are the lowest two energy levels of the proton $($in MeV $)?$

Hint: Find the two longest de Broglie wavelengths of the proton that can form standing waves in the box of length, $\backslash (\backslash$mathrm$\{$L$\}=10\backslash )$ fm$.$ Remember this from what we did for standing waves on a string: the wave must have nodes at the ends. Draw these, and then use these wavelengths to find the kinetic energies of the proton in these two states.

Part B

What is the wavelength $($in $\backslash (\backslash$mathbf$\{$n m$\}\backslash ))$ of a photon that is emitted by a nucleus when the proton makes a transition from the $\backslash (\backslash$mathbf$\{$n $=2\}\backslash )$ to the $\backslash (\backslash$mathbf$\{$n$\}=1\backslash )$ state $?$

Hint: Your answer should show that this is a photon in the gamma$-$ray part of the electromagnetic spectrum.

Incorrect; Try Again; $4$ attempts remaining