Question

According to Bohr's theory of the hydrogen atom, the total energy of the hydrogen atom with its electron revolving in the $n^{th}$ stationary orbit is proportional to

• A. $n$
• B. $n^2$
• C. $\frac{1}{n}$
  
• D. $\frac{1}{n^2}$

Answer 1

The correct option is D $\frac{1}{n^2}$

Total energy of the atom in the $n^{th}$ orbit is given by $E_n=-\frac{m{Z}^2{e}^4}{8{ϵ}_0^2{h}^2{n}^2}$
$\Rightarrow E_n\propto \frac{1}{n^2}$
Hence, the correct choice is (d).