Question

If $n>>1$, then the dependence of frequency of photon emitted as s result of transition of an electron from $nth$ orbit to $(n-1)th$ orbit, on $n$ will be

• A. $v\propto \frac{1}{n}$
• B. $v\propto \frac{1}{n^2}$
• C. $v\propto \frac{1}{n^3}$
• D. $v\propto \frac{1}{n^4}$

Answer 1

The correct option is C $v\propto \frac{1}{n^3}$

Therefore, $\nu \propto (\frac{1}{{n-1}^2}-\frac{1}{n^2})$

$\propto \left(\frac{n^2-{n-1}^2}{{n-1}^2\times n^2}\right)$

$\propto \frac{n^2-n^2-1+2n}{{\left(n(n-1)\right)}^2}asn>>1$

$\propto \frac{2n}{n^4}$

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