Atoms And Nuclei Question 307

Question: In a hydrogen like atom electron make 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:

Options:

A) $ \frac{1}{n} $

B) $ \frac{1}{n^{2}} $

C) $ \frac{1}{{}^{n^{3}}/{}_{2}} $

D) $ \frac{1}{n^{3}} $

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Answer:

Correct Answer: D

Solution:

  • $ \Delta E=hv $ $ v=\frac{\Delta E}{h}=k[ \frac{1}{{{( n-1 )}^{2}}}-\frac{1}{n^{2}} ]=\frac{k( 2n-1 )}{n^{2}( n^{2}-1 )} $ $ \approx \frac{2k}{n^{3}}\text{ or, }v\propto \frac{1}{n^{3}} $


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