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  • In a hydrogen like atom electron makes transition from an energy level with quantum number to another energy level with quantum number <img alt="(n-1)" src="/l

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

Option: 1

\frac{1}{n^2}


Option: 2

\frac{1}{n^3}


Option: 3

n^2


Option: 4

\frac{1}{n^4}


Answers (1)

best_answer

Energy of a hydrogen like atom is given as E_n=E_0 \cdot \frac{z^2}{n^2}

.E_{n-1}=E_0 \cdot \frac{z^2}{(n-1)^2} .

\text { frequency } \nu=\frac{\Delta E}{h}=\frac{-E_{n-1}+E_n}{h} \text {. }

\nu=\frac{1}{n} \cdot E_0 z^2\left[-\frac{1}{n^2}+\frac{1}{(n-1)^2}\right]

=\frac{E_0 z^2}{h}\left[\frac{n^2-(n-1)^2}{n^2(n-1)^2}\right]=\frac{E_0 z^2}{h}\left[\frac{(2 n-1)}{n^2(n-1)^2}\right]

=\frac{2 E_0 z^2}{h} \cdot\left(\frac{r}{n^3}\right) \text { (since } n>>1 \text { ) }

\Rightarrow \quad v\, \, \alpha^{-} \frac{1}{n^3}

Posted by

himanshu.meshram

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