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:
\(\begin{array}{l}v=\frac{e^{2}}{2\epsilon _{0}nh}\end{array} \)
The value of n in the ground state is 1.
Substituting the same in the above equation, we get
\(\begin{array}{l}v=\frac{e^{2}}{2\epsilon _{0}h}\end{array} \)
\(\begin{array}{l}\frac{v}{c}=\frac{e^{2}}{2\epsilon _{0}ch}\end{array} \)
\(\begin{array}{l}\frac{v}{c}=\frac{(1.6\times 10^{-19})^{2}}{2\times 8.85\times 10^{-12}\times 3\times 10^{8}\times 6.6\times 10^{-34}}\end{array} \)
\(\begin{array}{l}\frac{v}{c}=\frac{1}{137}\end{array} \)
