Question

The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr's orbit is:

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

Answer 1

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

The ratio of the difference in energy between the first and the second Bohr orbit:

$E_2-E_1=13.6\times {\left(1\right)}^2\times (\frac{1}{1^2}-\frac{1}{2^2})=13.6\times \frac{3}{4}$

The ratio of the difference in energy between the second and the third Bohr orbit:

$E_3-E_2=13.6\times {\left(1\right)}^2\times (\frac{1}{2^2}-\frac{1}{3^2})=13.6\times \frac{5}{36}$

$\frac{E_2-E_1}{E_3-E_2}=\frac{13.6\times \frac{3}{4}}{13.6\times \frac{5}{36}}=\frac{27}{5}$
Option D is correct.