Question

The expression for radius of a Bohr orbit in hydrogen atom is:

• A. $\frac{nh}{2\pi mr}$
• B. $\frac{n^2{h}^2}{4{\pi }^{2}m{e}^2}$
• C. $\frac{2{\pi }^{2}m{e}^4}{n^2{h}^2}$
• D. $\frac{n^2}{4{\pi }^{2}mh{e}^2}$

Answer 1

The correct option is B $\frac{n^2{h}^2}{4{\pi }^{2}m{e}^2}$

$mvr=\frac{nh}{2\pi }$

$\frac{m{v}^2}{r}=\frac{1}{4\pi E_0}\frac{e^2}{r^2}$

On solving these equations for v and r, we get-

$r=\frac{n^2{h}^2}{4{\pi }^{2}m{e}^2}$

Thus the correct answer is option $B$.