Question

When an electron makes transition from $(n+1)$ state, to $n$ state the wavelength of emitted radiations is related to $n$ $(n>>>1)$, according to $\lambda \propto n^x$. The value of $x$ is:

Answer 1

$E\propto -\frac{Z^2}{n^2}$ and
$\lambda =\frac{h}{mv}=\frac{h}{\sqrt{2mE}}$
so by calculation $\lambda \propto n^3$
So, $x$ is 3.