• # question_answer Which energy state of doubly ionized lithium $(L{{i}^{++}})$has the same energy as that of the ground state of hydrogen? Given Z for lithium = 3. A) $~n=1$                      B) $~n=2$C) $~n=3$                    D) $~n=4$

${{E}_{n}}=\frac{c{{z}^{2}}}{{{n}^{2}}}.$ For $n=1$state of hydrogen, we have ${{E}_{1}}=c$and for the nth state of $L{{i}^{++}},$we have ${{E}_{n}}=\frac{c{{.3}^{2}}}{{{n}^{2}}}=\frac{9c}{{{n}^{2}}}$             For ${{E}_{1}}={{E}_{n}}$we require Hence, the correction option is [c]. $C=\frac{9C}{{{n}^{2}}}$which gives $n=3.$Hence $n=3.$