Consider a hydrogen-like atom whose energy in nth excited state is given by
`E_(n) = (13.6 Z^(2))/(n^(2))`
When this excited makes a transition from excited state to ground state , most energetic photons have energy
`E_(max) = 52.224 eV`. and least energetic photons have energy
`E_(max) = 1.224 eV`
Find the atomic number of atom and the intial state or excitation.

Options

A. 2
B. 5
C. 4
D. None of these

Answer

A

Explanation

`(Delta E)_("max") " When " n rarr 1`
`(Delta E)_("min") " When " n rarr n-1`
`(E_(1))/(E_(2))- E_(1)= 52.224eV`
and `(E_(1))/(n^(2)) - (E_(1))/((n-1)^(2))= 1.224 eV`
By solving
`E_(1)= -54.4 eV and n= 5`
`E_(1)= (-13.6 Z^(2))/((1)^(2)) rArr - 54.4eV = (-13.6 Z^(2))/((1)^(2)) rArr Z= 2`