Question

What is the wavelength of the light emitted when an electron in a hydrogen atom undergoes transition from the energy level n = 4 to energy level n = 2? What is the colour corresponding to their wavelengths? (Given $R_H=109677c{m}^{-1}$)

• A. 486 nm, Blue
• B. 576 nm, Blue
• C. 650, Blue
• D. 450 nm, Blue

Answer 1

The correct option is A

486 nm, Blue

According to Balmer equation,
Wave number $\left(\overline{\nu }\right)=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}]c{m}^{-1}$
$n_1=2,n_2=4,R_H=109677c{m}^{-1}$
Substituting all the values, we get
$\overline{\nu }=109677[\frac{1}{(2{)}^2}-\frac{1}{(4{)}^2}]c{m}^{-1}=\frac{109677\times 3}{16}c{m}^{-1}$
Or $\lambda =\frac{1}{\overline{\nu }}=\frac{16}{109677\times 3}cm=486nm$
The wavelength corresponds to blue color.