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}} $
Show Answer
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}} $
