Question

The energy of second Bohr orbit of the hydrogen atom is $-328kJ$ ${mol}^{-1}$. Hence the energy of fourth Bohr orbit would be:

• A. $-41kJ$ ${mol}^{-1}$
• B. $-13121kJ$ ${mol}^{-1}$
• C. $-164kJ$ ${mol}^{-1}$
• D. $-82kJ$ ${mol}^{-1}$

Answer 1

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

According to the Bohr model, the energy of the orbit is inversely proportional to the square of orbit number:

$E\alpha 1/n²$ -------- (1)

$\frac{E_1}{E_2}=\frac{n_2}{n_1}$

$\frac{-328}{E_2}=\frac{4^2}{2^2}$

$E_2=\frac{-328kJ/mol}{4}$

$=-82kJ/mol.$

Hence, $-82kJ/mol$ is the answer.