# The hydrogen-like species $Li^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$ has one radial node and its energy is equal to the ground state energy of hydrogen atom. Energy of the state $S_1$ in units of the hydrogen atom ground state energy is

$(a)\;0.75\qquad(b)\;1.50\qquad(c)\;2.25\qquad(d)\;4.50$

$\large\frac{E_{S_1}}{E_{H_(ground)}}= \large\frac{-13.6\times9}{4\times(-13.6)}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= 2.25$