Question

When an electron jumps from the orbit $n = 2$ to $n = 4$, then wavelength of the radiations absorbed will be ($R$ is Rydberg's constant).

• A. $\frac {16}{3R}$
• B. $\frac {16}{5R}$
• C. $\frac {5R}{16}$
• D. $\frac {3R}{16}$

Answer 1

Answer: (A)

Wavelength, $\frac{1}{\lambda} =R\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
$\frac{1}{\lambda} =R\left[\frac{1}{(2)^{2}}-\frac{1}{(4)^{2}}\right]$
$\frac{1}{\lambda} =R\left[\frac{1}{4}-\frac{1}{16}\right]$
$\frac{1}{\lambda} =R\left[\frac{4-1}{16}\right]$
$\frac{1}{\lambda} =\frac{3 R}{16}$
$\lambda =\frac{16}{3 R}$