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

• A

  $802 \mathrm{~nm}$
• Correct answer
  B

  $823 \mathrm{~nm}$
• C

  $1882 \mathrm{~nm}$
• D

  $1648 \mathrm{~nm}$

Solution

The largest wavelength in the ultraviolet region of the hydrogen spectrum corresponds to the transition $n=2$ to $n=1$. That is,
The transition from $n=\infty$ to $n=3$ will produce the smallest wavelength in infrared region of the hydrogen spectrum. So,
Equations (i) and (ii) gives $\lambda=823.5 \mathrm{~nm}$

Hence, the correct answer is option: 'B'.