Question

The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where $e, h$, and $c$ have their usual meanings in cgs system)

• A. $2 \pi h c / e^{2}$
• B. $e r^{2} h / 2 \pi c$
• C. $e^{2} c / 2 \pi h$
• D. $2 \pi e^{2} / h c$

Answer 1

Answer: (D)

$v_{n}=k \frac{2 \pi e^{2}}{n h}$
We know that in cgs system $k=1$
$\therefore v_{n}=\frac{2 \pi e^{2}}{n h} $
$\Rightarrow v_{1}=\frac{2 \pi e^{2}}{h}$
So $\frac{v_{1}}{c}=\frac{2 \pi e^{2}}{c h}$