Q171 / 180 · KCET 2011 · Physics
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)
- Correct answerA$\frac{16}{3 R}$
- B$\frac{16}{5 R}$
- C$\frac{5 R}{16}$
- D$\frac{3 R}{16}$
Solution
Wavelength,
$$
\begin{aligned}
&\frac{1}{\lambda}=R\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right] \\
&\frac{1}{\lambda}=R\left[\frac{1}{(2)^{2}}-\frac{1}{(4)^{2}}\right] \\
&\frac{1}{\lambda}=R\left[\frac{1}{4}-\frac{1}{16}\right] \\
&\frac{1}{\lambda}=R\left[\frac{4-1}{16}\right] \\
&\frac{1}{\lambda}=\frac{3 R}{16} \\
&\lambda=\frac{16}{3 R}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.