The ratio of the speed of the electrons in th | vedclass

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(C) The speed of an electron in the $n^{	ext{th}}$ orbit of a hydrogen atom is given by $v = \frac{e^2}{2 \varepsilon_0 nh}$.For the ground state,$n

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$1 / 137$

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(C) The speed of an electron in the $n^{	ext{th}}$ orbit of a hydrogen atom is given by $v = \frac{e^2}{2 \varepsilon_0 nh}$.For the ground state,$n = 1$,so the speed is $v = \frac{e^2}{2 \varepsilon_0 h}$.The ratio of the speed of the electron to the speed of light $c$ is given by $\frac{v}{c} = \frac{e^2}{2 \varepsilon_0 ch}$.Substituting the values of the physical constants:$e = 1.6 	imes 10^{-19} 	ext{ C}$,$\varepsilon_0 = 8.85 	imes 10^{-12} 	ext{ F/m}$,$c = 3 	imes 10^8 	ext{ m/s}$,and $h = 6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}$.$\frac{v}{c} = \frac{(1.6 	imes 10^{-19})^2}{2 	imes 8.85 	imes 10^{-12} 	imes 3 	imes 10^8 	imes 6.63 	imes 10^{-34}} \approx \frac{1}{137}$.

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

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