Question

The speed of an electron in first Bohr orbit is $\frac{c}{137}$,. The speed of electron in third Bohr orbit of hydrogen will be

• A. $\frac{c}{137}$
• B. $\frac{3c}{137}$
• C. $\frac{c}{3\times 137}$
• D. $\frac{9c}{137}$

Answer 1

Answer: (C)

$\frac{c}{3\times 137}$

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

$v=\frac{nh}{mr}$

Also $r=0.526n^2$

This gives $v=\frac{h}{2\pi mn\times .526}$

So, the $v\propto 1/n$

So when $n=3$, $\Rightarrow v=\frac{c}{(137\times 3)}$