Question

Find the ratio of the difference in energy between the first and the second Bohr's orbit to that between the second and third Bohr's orbit of a hydrogen atom.

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{4}{9}$
• D. $\frac{27}{5}$

Answer 1

The correct option is D $\frac{27}{5}$

Energy of the $n^{th}$ Bohr's orbit is given by
$E_n=-13.6\times \frac{Z^2}{n^2}eV$
For H-atom, Z = 1
The difference in energy between the first and the second Bohr orbit:
$E_2-E_1=13.6\times 1^2\times (\frac{1}{1^2}-\frac{1}{2^2})$
$=13.6\times \frac{3}{4}eV$
The difference in energy between the second and the third Bohr orbit:
$E_3-E_2=13.6\times 1^2\times (\frac{1}{2^2}-\frac{1}{3^2})$
$=13.6\times \frac{5}{36}eV$
Taking the ratio, we get :
$\frac{E_2-E_1}{E_3-E_2}=\frac{13.6\times \frac{3}{4}}{13.6\times \frac{5}{36}}=\frac{27}{5}$