Question

What is the ratio of wavelength of radiations emitted, when an electron in hydrogen atom jumps from fourth orbit to second orbit and from third orbit to second orbit?

• A. 27 : 25
• B. 20 : 27
• C. 20 : 25
• D. 25 : 27

Answer 1

The correct option is B 20 : 27

The wavelength $\left(\lambda \right)$ of spectral line is
given by
$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
When electron jumps from fourth, orbit to second orbit,
$\frac{1}{{\lambda }_1}=R(\frac{1}{2^2}-\frac{1}{4^2})=R\times \frac{3}{16}$
or ${\lambda }_1=\frac{16}{3R}$
When electron jumps from third orbit to second orbit,
$\frac{1}{{\lambda }_2}=R(\frac{1}{2^2}-\frac{1}{3^2})=R\times \frac{5}{36}$
${\lambda }_2=\frac{36}{5R}$
Hence, $\frac{{\lambda }_1}{{\lambda }_2}=\frac{16}{3R}\times \frac{5R}{36}=\frac{20}{27}$
Note The electron may jump over to an outer orbit of higher energy. This process in which absorption of energy by an electron takes the electron from an inner orbit to some outer orbit of higher energy is called excitation.