Question

The velocity of electron in first orbit of $H$-atom as compared to the velocity of light is :

• A. $\frac{1}{10}$th
• B. $\frac{1}{100}$th
• C. $\frac{1}{1000}$th
• D. same

Answer 1

Answer: (B)

Velocity of light $=3\times 10^{10}cm/sec$.
Velocity of an electron in the orbit is given by the expression,
$v=\frac{nh}{2\pi mr}$,
where, $h$ is Planck's constant $=6.6256\times 10^{-34}Js$.
$m$ is mass of electron $=9.1096\times 10^{-31}kg$.
$r$ is radius of orbit $=0.529\times 10^{-10}\times n^{2}m$.
For $1^{\text{st }}$ orbit of H-atom, $r=0.529\times 10^{-10}\times 1^{2}m$.
Substituting these values in the expression of velocity, we get v $=2.18\times 10^{8}cm/sec$.
Comparing the velocity of the first orbit of $H$-atom with the velocity of light, we get to know that velocity of the first orbit of $H$ - atom is $\frac{1}{100}$ th of the velocity of light.