# The ratio of the speed of the electron in the ground state of hydrogen atom to the speed of light is

The ratio of the speed of an electron in the ground state of H atom to speed of light is 1/137.

Explanation:

Speed of electron in the nth orbit for the hydrogen atom is given as:

$$v=\frac{e^{2}}{2\epsilon _{0}nh}$$

The value of n in the ground state is 1.

Substituting the same in the above equation, we get

$$v=\frac{e^{2}}{2\epsilon _{0}h}$$ $$\frac{v}{c}=\frac{e^{2}}{2\epsilon _{0}ch}$$ $$\frac{v}{c}=\frac{(1.6\times 10^{-19})^{2}}{2\times 8.85\times 10^{-12}\times 3\times 10^{8}\times 6.6\times 10^{-34}}$$ $$\frac{v}{c}=\frac{1}{137}$$