The ratio of total energy of an orbiting electron in 3rd orbit to that in and 5th orbit in a hydrogen atom is

25 : 9

The correct answer is Option (2) → 25 : 9

Total energy of an electron in nth orbit of hydrogen atom:

$E_n = - \frac{13.6}{n^2}\ \text{eV}$

For 3rd orbit, $E_3 = - \frac{13.6}{3^2} = - \frac{13.6}{9}$

For 5th orbit, $E_5 = - \frac{13.6}{5^2} = - \frac{13.6}{25}$

Ratio of total energies (3rd to 5th orbit):

$\frac{E_3}{E_5} = \frac{-13.6/9}{-13.6/25} = \frac{25}{9}$

Ratio of total energy = 25 : 9