The hydrogen -like species `Li^(2+)` is in a spherically sysmmetric state `S_(1)` with one node ,Upon ansorbing light , the ion undergoes transition to a state `S_(2)` The state `s_(2)` has one radial node and its energy is equal is to the ground state energy of the hydrogen atom
Energy of the state `S_(1)` in units of the hydrogen atom ground state enegy is

Options

A. 0.75
B. 1.5
C. 2.25
D. 4.5

Answer

C

Explanation

`E_(n) = (-13.6)/(n^(2))Z^(2)`
For ground state of H atom
`E_(H) = (-13.6)/(1^(2)) xx 1^(2)`
For `2s` of `Li^(2+)`
`E_(Li^(2+)) = (-13.6)/(2^(2)) xx 3^(2)`
`E_(Li^(2+))/(E_(H)) = ((-13.6)/(4) xx 9)/(-13.6) = 2.29`
or `E_(Li^(2+)) = 2.25E_(H)`