JEE Advanced 2021 · Paper 1 · Physics Q14

PhysicsMultiple correct+4 / -2Question 14 of 57

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5

There is an overlap between the wavelength ranges of Balmer and Paschen series

The wavelengths of Lyman series are given by

\left(1 + \dfrac{1}{m^2}\right)\lambda_0

, where

\lambda_0

is the shortest wavelength of Lyman series and

m

is an integer

The wavelength ranges of Lyman and Balmer series do not overlap

Answer and worked solution

Official answer: A, D

Rydberg formula. $\frac1\lambda=R\left(\frac1{n_1^2}-\frac1{n_2^2}\right)$ .

Check each option.

(A) Balmer: the longest wavelength is $\frac{36}{5R}$ and the shortest is $\frac4R$ . Their ratio is $\frac95$ . True.
(B) Balmer spans about 365-656 nm and Paschen about 820-1875 nm. They do not overlap. False.
(C) Lyman: $\lambda=\frac{\lambda_0}{1-1/m^2}=\frac{m^2}{m^2-1}\lambda_0$ , not $\left(1+\frac1{m^2}\right)\lambda_0$ . False.
(D) Lyman spans about 91-122 nm and Balmer about 365-656 nm. They do not overlap. True.

(A), (D)

Topics:Bohr model and hydrogen spectrum

JEE Advanced 2021 · Paper 1, Physics question 14