CBSE Class 12 Physics 2023 Outside Delhi Set 1 Paper - Question ...

CBSE Class 12 Physics 2023 Outside Delhi Set 1 Paper

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Question : 11 of 35

Marks: +1, -0

A hydrogen atom makes a transition from

n=5

to

n=1

orbit. The wavelength of photon emitted is

λ

. The wavelength of photon emitted when it makes a transition from

n=5

to

n=2

orbit is

$\;{8}/{7} λ$
$\;{16}/{7} λ$
$\;{24}/{7} λ$
$\;{32}/{7} λ$

Solution:

In

1^{\;\text "st "\;}

case

\;\;{1}/{λ}\;= {\R} [\;{1}/{1^2}-\;{1}/{5^2}]

\;\text " or, "\;\;\;{1}/{λ}\;= {\R} [1-\;{1}/{25}] = {\R} [\;{24}/{25}]

∴ \; {\R}\;=\;{25}/{24} × \;{1}/{λ}

In

2^{\;\text "nd "\;}

case

{1}/{λ^{'}}\;= {\R} [\;{1}/{2^2}-\;{1}/{5^2}]

\;\text " or, "\; \;\; \;{1}/{λ^{'}}\;= {\R} [\;{1}/{4}-\;{1}/{25}] = {\R} × \;{21}/{100}

\;\text " or, "\;\;\;{1}/{λ^{'}}\;=\;{25}/{24} × \;{1}/{λ} × \;{21}/{100}

\;\text " or, "\;\;\;{1}/{λ^{'}}\;=\;{21}/{96 λ}

∴ \;λ^{'}\;=\;{96}/{21} λ=\;{32}/{7} λ

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