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

The hydrogen -like species `Li^(2+)` is in a spherically symmetric sta

1.	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 isA. `0.75`B. `1.50`C. `2.25`D. `4.50`
Answer» 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`

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