$($a$)$ Find the radius of the n $=6$ Bohr orbit of a doubly ionized lithium atom $($Li$2+,$ Z $=3).$

m

$($b$)$ Is the energy required to raise an electron from the n $=6$ state to the n $=8$ state in Li$2+$ greater than, less than, or equal to the energy required to raise an electron in hydrogen from the n $=6$ state to the n $=8$ state?

$|$Eion$|<|$EH$|-$ smaller force on Li$2+$ electron due to greater distance from nucleus$|$Eion$|<|$EH$|-$ greater force on Li$2+$ electron due to larger number of protons$|$Eion$|>|$EH$|-$ smaller force on Li$2+$ electron due to increased distance from nucleus$|$Eion$|>|$EH$|-$ greater force on Li$2+$ electron due to larger number of protons$|$Eion$|=|$EH$|-$ same n interval in two hydrogen$-$like atoms

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