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Line spectra of hydrogen atoms

Which of the following statement(s) is(are) correct about the

Question

Hard

Solving time: 4 mins

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

SELECT MULTIPLE OPTION

A

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

9/5

.

B

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

C

The wavelengths of Lyman series are given by

(1 + \frac{1}{m ^{2}}) λ_{0}

. where

λ_{0}

is the shortest wavelength of Lyman series and

m

is an integer.

D

The wavelength ranges of Lyman and Balmer series do not overlap.

Views: 5,952 students

Updated on: Oct 11, 2022

Exam:

JEE Advanced 2021

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

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Text solutionVerified

For (a) When the transition is from any level to

n = 2

, then photon emitted belong to Balmer series.

∴

For longest wavelength, transition occurs from

n = 3

to

n = 2

.

∴ \frac{h c}{λ _{m a x}} = R c h [\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}]

and for shortest wavelength, transition occurs from

n = \infty

to

n = 2

∴ ∴ \frac{h c}{λ _{min}} = R ch [\frac{1}{2 ^{2}} - \frac{1}{\infty ^{2}}] \frac{λ _{longest}}{λ _{shortest}} = \frac{9}{5}

For (b)

λ_{bongest} of Balmer = \frac{36}{5 R} λ_{shortest} of Paschen = \frac{9}{R}

Hence, these wavelength don't overlap.
For (c)

\frac{1}{λ} = R [\frac{1}{1} - \frac{1}{m ^{2}}]

Also,

\frac{1}{λ _{0}} = R

∴ \frac{1}{λ} = \frac{1}{λ _{0}} [1 - \frac{1}{m ^{2}}] \Rightarrow λ = \frac{λ _{0}}{1 - \frac{1}{m ^{2}}}

For (d)

λ_{longest} of Lyman = \frac{4}{3 R}, λ_{shortest} of Balmer = \frac{4}{R}

Hence, that wavelength don't overlap.

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Question Text	Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?
Updated On	Oct 11, 2022
Topic	Atoms
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	163
Avg. Video Duration	3 min