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