Question

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

• A. $\frac{1}{n^2}$
• B. $\frac{1}{n^{3/2}}$
• C. $\frac{1}{n^3}$
• D. $\frac{1}{n}$

Answer 1

Answer: (C)

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

$\Delta E=h\mu$

$\mu =\frac{\Delta E}{h}=k[\frac{1}{(n-1{)}^2}-\frac{1}{n^2}]$ $=\frac{2kn}{n^2(n-1{)}^2}$ which is approximately equal to $\frac{1}{n^3}$