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_(min) = 1.224 eV`
Find the atomic number of atom and the initial state or excitation.

Options

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

Answer

A

Explanation

Maximum energy is liberated for transition `E_(n) rarr E_(1)` and minimum energy for `E_(n) rarr E_(n-1)`
Hence `(E_(1))/(n^(2)) - E_(1) = 52.224 eV` and `(E_(1))/(n^(2)) - (E_(1))/((n-1)^(2)) = 1.224 eV rArr E_(1) = -54.4 eV` and `n = 5`
Now `E_(1) = - (13.6Z^(2))/(1^(2)) = - 54.4 eV`. Hence `Z = 2`