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Question

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a0 is the radius of the ground state orbit, m is the mass and e is charge of the electron and ϵ0 is the vacuum permittivity, the speed of the electron is

A
\N
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B
eϵ0 a0 m
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C
e4πϵ0 a0 m
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D
4πϵ0 a0 me
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Solution

The correct option is C e4πϵ0 a0 m

Centripetal force= force of attraction of nucleus on electron

mv2a0=14πϵ0e2a20

v = e4πϵ0m a0


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