Question

A sample of hydrogen atoms in ground state is exposed to electromagnetic radiation of $1019\stackrel{o}{\text{A}}$. The wavelengths of the induced radiation(s) (radiations emitted when electron returns to the ground state) is/are:
$(\text{Given,}R=1.09\times {10}^7{\text{m}}^{-1})$

• A. $1028\stackrel{o}{\text{A}}$
• B. $1207.7\stackrel{o}{\text{A}}$
• C. $6521.6\stackrel{o}{\text{A}}$
• D. $190.4\stackrel{o}{\text{A}}$

Answer 1

Answer: (B), (C)

$6521.6\stackrel{o}{\text{A}}$

We know that,
$\frac{1}{\lambda }=R{Z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
Since electron is in ground state, $n_1=1$.
Substituting the values, we get,
$\Rightarrow \frac{1}{1019\times {10}^{-10}\text{m}}=1.09\times {10}^7\times 1^1(\frac{1}{1^2}-\frac{1}{n^2})$
$\Rightarrow 1-\frac{1}{n^2}=0.9$
$\Rightarrow n_2\approx 3$

$\because {\lambda }_1=1019\stackrel{o}{\text{A}}$
$\frac{{\lambda }_2}{{\lambda }_1}=\frac{(\frac{1}{1^2}-\frac{1}{3^2})}{(\frac{1}{2^2}-\frac{1}{3^2})}$
$\Rightarrow {\lambda }_2=6521.6\stackrel{o}{\text{A}}$

$\frac{{\lambda }_3}{{\lambda }_1}=\frac{(\frac{1}{1^2}-\frac{1}{3^2})}{(\frac{1}{1^2}-\frac{1}{2^2})}$
$\Rightarrow {\lambda }_3=1207.7\stackrel{o}{\text{A}}$.