$[8]$ One can use the Bohr Model to determine the electronic energy levels for a Helium ion, He$+$ because

this ion has a single electron. The Bohr Model energy equation must account for the increase in atomic

number from $Z=1$ for Hydrogen to $Z=2$ for Helium. Consider the He$+$ ions are all initially excited to $n=4.$

a$)$ Draw the Bohr orbitals for a $He+$ ion with the single electron in $n=4.$ Using arrows, show all the possible

de$-$excitation $($downwards$)$ transitions that this electron could make.

b$)$ Write the general equation for the total electronic energy levels of a $He+$ ion.

c$)$ Calculate the wavelengths for all the possible de$-$excitation transitions resulting in a photon being

emitted.

d$)$ Use these wavelengths to sketch the emission line spectra for the $H{e}^{+}$ions, similar to the hydrogen

emission spectrum shown below. The sketch should be to scale.