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

Options

A. `1//2`
B. `2//137`
C. `1//137`
D. `1//237`

Answer

C

Explanation

Let the speed of electron in `n^(th)` orbit of atom be `v_(n)`.
We know, `v_(n) = (Ze^(2))/(2epsilon_(0)nh)`
For ground state, n = 1
`v_(1) = e^(2)/(2epsilon_(0) xx 1 xx h)`
`v_(1)/c = (e^(2)/(2 epsilon_(0)h) (1/c))`
`(v_(1)/c) = ((1.6 xx 10^(-19)) xx (1.6 xx 10^(-19)))/(2 xx 8.85 xx 10^(-12) xx 6.63 xx 10^(-34) xx 3 xx 10^(8))`
`(v_(1))/c = 1/137`