Question

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

• A. $\frac{h}{\pi }$
• B. $\frac{h}{2\pi }$
• C. $\frac{3h}{2\pi }$
• D. $\frac{h}{\pi }$

Answer 1

The correct option is A $\frac{h}{\pi }$

The energy of an electron in $n^{th}$ orbit is given by
$E=-13.6\times \frac{Z^2}{n^2}$
For hydrogen atom, $Z=1$ and energy is given as $-3.4eV$
Hence, putting these values
$-3.4=-13.6\times \frac{1}{n^2}$
This gives $n=2$

Now the angular momentum in $n^{th}$ orbit
= $\frac{nh}{2\pi }=\frac{h}{\pi }$