The hydrogen -like species `Li^(2+)` is in a spherically symmetric state `S_(1)` with one node. Upon absorbing 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 energy is

Options

A. `0.75`
B. `1.50`
C. `2.25`
D. `4.50`

Answer

C

Explanation

Spherically symmetrical state (i.e.s orbital ) with one radial node `= 2s = s_(1)`
`(n- l- 1) `
`n = 2 rarr s_(2)("one nodial node") = n_(2)`
and `(E_(n))_(li^(2+)) = (E)_(1H)`
`rArr -13.6 xx (3^(2))/(n_(2)^(2))= -13.6 xx (1^(2))/(1^(2))`
`rArr n_(2) = 3`
` rArr s_(2) = 3p`
`rArr (E_(s_(1))/(E_(H)))_(n=1)= (-13.6 xx (3^(2))/(2^(2)))/(-13.6 xx (1^(2))/(1^(2))) = 2.25`