Question

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

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

Answer 1

Answer: (A)

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

Answer 2

In a hydrogen like atom, when an electron makes an transition from an energy level with n to n - 1, the frequency of emitted radiation is
$\upsilon=RcZ^{2}\left[\frac{1}{\left(n-1\right)^{2}}-\frac{1}{n^{2}}\right]=\frac{RcZ^{2}\left(2n-1\right)}{n^{2}\left(n-1\right)^{2}}$
As n > > 1
$\therefore\quad\upsilon=\frac{RcZ^{2} 2N}{n^{4}}=\frac{2RcZ^{2}}{n^{3}}$ or $\upsilon\propto\frac{1}{n^{3}}$