Q. 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) $802\ nm$
B) $823\ nm$
C) $1882\ nm$
D) $1648\ nm$
Explanation
(b) $\frac{1}{122nm} = R\left( \frac{1}{1^{2}} - \frac{1}{2^{2}} \right) = \frac{3R}{4}$
$\Rightarrow \frac{1}{\lambda} = R\left( \frac{1}{3^{2}} - \frac{1}{\infty^{2}} \right) = \frac{R}{9} \Rightarrow \frac{\lambda}{122} = \frac{3}{4} \times 9 = \frac{27}{4}$
$\Rightarrow \lambda = 823\ nm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.