Question

The energy of second Bohr orbit of the hydrogen atom is $328kJmo{l}^{-1}$, hence the energy of fourth Bohr orbit would be:

• A. $-41kJmo{l}^{-1}$
• B. $-1312kJmo{l}^{-1}$
• C. $-164kJmo{l}^{-1}$
• D. $-82kJmo{l}^{-1}$

Answer 1

The correct option is D $-82kJmo{l}^{-1}$

Energy (E) of a bohr orbit in hydrogen atom in Joules :
$E=-K\left(\frac{Z^2}{n^2}\right)K=2.18\times {10}^{-18}$
So, for hydrogen:
$E\propto \frac{1}{n^2}$

$\frac{E_4}{E_2}={\left(\frac{n_2}{n_4}\right)}^2$
$E_4=-328\times {\left(\frac{2}{4}\right)}^2$
$E_4=-82kJmo{l}^{-1}$