Which statement is true.

Options

A. Spacing between energy levels `n = 1` and `n = 2` in hydrogen atom is greater than that of `n = 2` and `n = 3`
B. Spacing between energy levels `n = 1` and `n= 2` in hydrogen atom is equal to that `n = 2` and `n = 3`
C. Spacing between energy levels `n = 1` and `n = 3` in hydrogen atom is less than that of `n = 2` and `n = 3`
D. None

Answer

A

Explanation

(a) `E_n = - (13.6 Z^2)/(n^2) eV`
`Delta E_1 rarr 2 = - (13.6)/(2^2) +(13.6)/(1^2) = 10.2 eV`
`Delta E_2 rarr 3 = - (13.6)/(3^2) + (13.6)/(2^2) = 1.9 eV`
`:.` One moving from lower value of `n` to higher value of `n` energy difference between sucessive energy levels decreases.