The ratio of total energy of an orbiting electron in 3rd orbit to that in 5th orbit in a hydrogen atom is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 25 : 9 \)
In the Bohr model the total energy of the electron in the \( n \)th orbit of hydrogen varies as the inverse square of \( n \).
\( \displaystyle E_{n} = -\frac{13.6\,\mathrm{eV}}{n^{2}} \;\Rightarrow\; E_{n} \propto \frac{1}{n^{2}} \)
\( \displaystyle \frac{E_{3}}{E_{5}} = \frac{5^{2}}{3^{2}} = \frac{25}{9} \)
So the ratio is \( 25 : 9 \). The 3rd orbit is lower in energy, so its (negative) energy has the larger magnitude.