Question

The energy of second Bohr orbit of the hydrogen atom is $-328{\text{kJ mol}}^{-1}$; hence the energy of fourth Bohr orbit would be

• A. $-41{\text{kJ mol}}^{-1}$
• B. $-1312{\text{kJ mol}}^{-1}$
• C. $-164{\text{kJ mol}}^{-1}$
• D. $-82{\text{kJ mol}}^{-1}$

Answer 1

The correct option is D $-82{\text{kJ mol}}^{-1}$

From Bohr's theory, if an electron of an hydrogen atom, orbits in orbit ${}^{\prime }{n}^{\prime }$ with energy ${}^{\prime }{E}_n^{\prime }$, then, $E_n\propto \frac{1}{n^2}$
Since, Z = 1 for H-atom
So,
Ratio of energies for $2^{nd}$ orbit $(n_2=2)$ and $4^{th}$ orbit $(n_4=4)$ is,
$\frac{E_2}{E_4}=\frac{n_4^2}{n_2^2}=\frac{4}{1}$
$\therefore E_4=\frac{E_2}{4}=-82KJmo{l}^{-1}$