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

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

Tardigrade Admin · Accepted Answer

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}}{( \frac{1}{1 ^{2}} - \frac{1}{2 ^{2}} )}

... (i).
The smallest wavelength in the infrared region corresponds to a maximum energy of the Paschen series.

λ = \frac{\frac{1}{R}}{( \frac{1}{3 ^{2}} - \frac{1}{\infty} )}

.... (ii)
Solving Eqs. (i) and (ii), we get

λ = 823.5 nm

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

$802 nm$

$823 nm$

$1882 nm$

$1648 nm$

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

802nm

823nm

1882nm

1648nm

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

$802 nm$

$823 nm$

$1882 nm$

$1648 nm$