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

Ans: (B)

Sol: In hydrogen spectrum series U-V region is Lymen Series .

The Largest wavelength occurs in transition from n=2 to n=1

$\large \frac{1}{122} = R (\frac{1}{1^2} – \frac{1}{2^2} )$ …(i)

The smallest wavelength in infrared region corresponds to

$\large \frac{1}{\lambda} = R (\frac{1}{3^2} – \frac{1}{\infty} )$ …(ii)

On solving (i) & (ii) we get λ = 823 nm