$\frac{m v^{2}}{r}=\frac{K z e^{2}}{r^{2}}$
or $\quad \frac{1}{2} m v^{2}=\frac{K z e^{2}}{2 r}= KE$
and $\quad PE =-\frac{K z e^{2}}{r}$
$\therefore$ Total energy $= KE + PE$
$=\frac{K z e^{2}}{2 r}-\frac{K z e^{2}}{r}=-\frac{1}{2} \frac{K z e^{2}}{r}$
Given, $\quad E=\frac{-E_{0}}{n}$
Comparing given equation, we get
$r \propto n$
$\text { As, } \quad KE \propto \frac{1}{r} \propto \frac{1}{n} (\because r \propto n)$
$\Rightarrow v^{2} \propto \frac{1}{n} \text { or } \quad v \propto \frac{1}{\sqrt{n}}$
$\text { Since, angular momentum, } L=m v r$
$\text { or } L \propto v r$
$\text { or } L \propto \frac{1}{\sqrt{n}} n$ $\quad(\because r \propto n)$
$\text { or } L \propto \sqrt{n}$
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