In the Bohr model of a hydrogen atom,the cent | vedclass

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(C) The centripetal force required for the circular motion of the electron is provided by the electrostatic Coulomb force between the proton and the e

Vedclass · Accepted Answer

$\frac{e}{{\sqrt {4\pi {\varepsilon _0}{a_0}m} }}$

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(C) The centripetal force required for the circular motion of the electron is provided by the electrostatic Coulomb force between the proton and the electron.Equating the centripetal force to the Coulomb force:$\frac{m{v^2}}{{a_0}} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{e^2}}}{{a_0^2}}$Canceling $a_0$ from both sides:$m{v^2} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{e^2}}}{{a_0}}$Solving for $v^2$:${v^2} = \frac{{{e^2}}}{{4\pi {\varepsilon _0}{a_0}m}}$Taking the square root of both sides,we get the speed of the electron:$v = \frac{e}{{\sqrt {4\pi {\varepsilon _0}{a_0}m} }}$Thus,the correct option is $C$.

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