$[1/2\mathrm{.}5$ Points$]$

$($a$)$ Find the radius of the $n=4$ Bohr orbit of a doubly ionized lithium atom $(L^{2+},Z=3).$

$2\mathrm{.}821$E$-10$

m

$($b$)$ Is the energy required to raise an electron from the $n=4$ state to the $n=5$ state in $L{i}^{2+}$ greater than, less than, or equal to the energy required to raise an electron in hydrogen from the $n=4$ state to the $n=5$ state?

smaller force on $L{i}^{2+}$ electron due to greater distance from nucleus

greater force on $L{i}^{2+}$ electron due to larger number of protons

$|E_{\text{i}\text{o}\text{n}}|>|E_H|-$smaller force on $L^{2+}$ electron due to increased distance from nucleus

$|E_{\text{i}\text{o}\text{n}}|>|E_H|-$ greater force on $L{i}^{2+}$ electron due to larger number of protons

$|E_{\text{i}\text{o}\text{n}}|=|E_H|-$ same $n$ interval in two hydrogen$-$like atoms

$($c$)$ Verify your answer to part $($b$)$ by calculating the relevant energies.

$E_{L^{+}+}=$

$E_H=($ work on PART C ONLY$)$