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  • The ratio of the speed of an electron in the ground state of hydrogen atom to the speed of light in vacuum is:  Option: 1 <img alt="\f

The ratio of the speed of an electron in the ground state of hydrogen atom to the speed of light in vacuum is:

 

Option: 1

\frac{1}{137}


Option: 2

\frac{2}{137}


Option: 3

\frac{1}{237}


Option: 4

\frac{2}{237}


Answers (1)

best_answer

Speed of an electron in the ground state of hydrogen atom is

\mathrm{\mathrm{v}=\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi \mathrm{e}^2}{\mathrm{~h}}=\mathrm{c}\left(\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi \mathrm{e}^2}{\mathrm{ch}}\right)=\alpha \mathrm{c}=\frac{\mathrm{c}}{137}}

Where c = speed of light in vacuum

\begin{aligned} & \alpha=\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi \mathrm{e}^2}{\mathrm{ch}}=\frac{1}{137}=\text { Fine structure constant } \\ \\& \therefore \quad \frac{\mathrm{v}}{\mathrm{c}}=\frac{1}{137} \end{aligned}

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Rishabh

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