Question

The $122nm$ is the largest wavelength in the ultraviolet region of the hydrogen spectrum. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is:

• A. $802nm$
• B. $823nm$
• C. $1882nm$
• D. $1648nm$

Answer 1

Answer: (B)

The series in the UV region is Lyman series. Longest wavelength corresponds to minimum energy which occurs in the transition from $n=2$ to $n=1$ .
Therefore, $122=\frac{\frac{1}{R}}{\left(\frac{1}{1^{2}} - \frac{1}{2^{2}}\right)}$ ... ( $i$ )
The smallest wavelength in the infrared region corresponds to a maximum energy of the Paschen series.
$\lambda = \frac{\frac{1}{\text{R}}}{\left(\frac{1}{3^{2}} - \frac{1}{\infty }\right)}$ .... ( $ii$ )
Solving equations ( $i$ ) and ( $ii$ ), we get,
$\lambda =823.5nm$ .