Question

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

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

Answer 1

Answer: (B)

The series in UV region is Lyman series. Longest wavelength corresponds to minimum energy which occurs in the transition from n = 2 to n = 1.
Therefore $122 = \frac{\frac{1}{R}}{\left(\right. \frac{1}{1^{2}} - \frac{1}{2^{2}} \left.\right)}$ ... (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 Eqs. (i) and (ii), we get
$\lambda =823.5nm$