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, e is the charge on the elytron and $ε_{0}$ is the vacuum permittivity, the speed of the electron is :

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$\frac{e}{\sqrt{ε_{0} a_{0} m}}$

$\frac{e}{\sqrt{4 {πε}_{0} a_{0} m}}$

$\frac{\sqrt{4 {πε}_{0} a_{0} m}}{e}$

Zero

answer is C.

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Detailed Solution

Centripetal force = Coulombs force.

$\frac{{mv}^{2}}{a_{0}} = \frac{1}{4 {πϵ}_{0}} \frac{e^{2}}{a_{0}^{2}}$

$\Rightarrow v = \frac{e}{\sqrt{4 {πϵ}_{0} {ma}_{0}}}$

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