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The ratio of the speed of the electrons ...

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

A

`1/2`

B

`2/137`

C

`1/137`

D

`1/237`

Text Solution

Verified by Experts

The correct Answer is:
C
Speed of electron in `n^(th)` orbit of hydrogen atom `v= e^2/(2epsilon_0nh)`
In ground state `n = 1implies v = (e^2)/(2epsilon_0h)`
`implies v/c = e^2/(2epsilon_0ch)=((1.6 xx10^(-19))^2)/(2 xx8.85 xx10^(-12)xx3xx10^8xx6.6 xx10^(-34))=1/137`
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