Question

For Balmer series in the spectrum of hydrogen, the wave number of each line is given by
$\overline{v}=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$ where $R_H$ is constant and $n_1,n_2$ are integers, which of the following statements is (are) correct?
1. As wavelength decreases, the lines in the series converge.
2. The integer $n_1$ is equal to $2$.
3. The ionization energy of hydrogen can be calculated from the wave number of these lines.
4. The lines of longest wavelength corresponds to $n_2=3$.

• A. 1, 2 and 3
• B. 2, 3 and 4
• C. 1, 2 and 4
• D. 2 and 4
• E. 2 only

Answer 1

The correct option is C 1, 2 and 4

$\overline{v}=\frac{1}{\lambda }=R_H[\frac{1}{2^2}-\frac{1}{n_2^2}]$

Here $n=2$ since Balmer series, the transition is between some energy level $n_2$ and $n_1=2$.As the wave length decreases, the wave number increases. This implies that the difference $\frac{1}{2^2}-\frac{1}{n_2^2}$ also increases or ultimately $m_2$ increases. As $n_2$increases , the lines in the series covrege.

Ionization energy of hydrogen can be calculated from wave number of lines in lyman series as the electron is present in $n=1$.Longest wave length corresponds to minimum difference betweeen $\frac{1}{2^2}$ and $\frac{1}{n_2^2}$. This is for $n_2=3.$