Question

An electron in Bohr's hydrogen atom has an energy of -3.4 $eV$. The angular momentum of the electron is

• A. $h/\pi$
• B. $h/2\pi$
• C. $5h/2\pi$
• D. $2h/\pi$

Answer 1

The correct option is A $h/\pi$

The energy of an electron in an orbit of principal quantum number $n$ is given as
$E=\frac{-13.6}{n^2}eV\Rightarrow -3.4eV=\frac{-13.6}{n^2}eV\Rightarrow n^2=4\mathrm{Gives}\mathrm{us}n=2$
The angular momentum of an electron in $n^{th}$ orbit is given as
$L=\frac{nh}{2\pi }\mathrm{Putting}n=2\mathrm{we}\mathrm{obtain}L=\frac{2h}{2\pi }=\frac{h}{\pi }$