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Bohr Model of the Hydrogen Atom

In a hydrogen like atom electron makes transition from an ener

Question

Hard

Solving time: 4 mins

In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1$ , the frequency of radiation emitted is proportional to :

\frac{1}{n ^{2}}

\frac{1}{n ^{3}}

n^{2}

\frac{1}{n ^{4}}

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Updated on: Sep 24, 2023

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In a hydrogen like atom electron makes transition from an energy level with quantum number

n

to another with quantum number

(n - 1)

. If

n >> 1

, the frequency of radiation emitted is proportional to :

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

E_{n} - E_{n - 1} Z^{2}

= - 13.6 n ^{2} + \frac{- 13.6 Z ^{2}}{( n - 1 ) ^{2}}

= 13.6 Z^{2} [\frac{1}{( n - 1 ) ^{2}} - \frac{1}{n ^{2}}]

h v = 13.6 Z^{2} [\frac{n ^{2} - ( n - 1 ) ^{2}}{n ^{2} ( n - 1 ) ^{2}}]

= \frac{13.6 Z ^{2}}{n ^{2}} [\frac{1}{( 1 - 1/ n ) ^{2}} - 1]

= \frac{13.6 Z ^{2}}{n ^{2}} [(1 - \frac{1}{n})^{- 2} - 1]

= \frac{13.6 Z ^{2}}{n ^{2}} [1 + \frac{2}{n} - 1] = \frac{2 \times 13.6 Z ^{2}}{n ^{3}} v \propto \frac{1}{n ^{3}}

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Question Text	In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1$ , the frequency of radiation emitted is proportional to :
Updated On	Sep 24, 2023
Topic	Atoms
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 8
Upvotes	793
Avg. Video Duration	8 min

In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1$ , the frequency of radiation emitted is proportional to :

Text solutionVerified

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In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n−1). If n>>1, the frequency of radiation emitted is proportional to :

Text solutionVerified

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In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1$ , the frequency of radiation emitted is proportional to :