Q: In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a_{0} is the radius of the ground state orbit m is the mass, e is the charge on the electron and ε_{0} is the vacuum permittivity, the speed of the electron is

(a) 0

(b) $\frac{e}{\sqrt{\epsilon_0 a_0 m}}$

(c) $\frac{e}{\sqrt{4 \pi \epsilon_0 a_0 m}}$

(d) $\sqrt{\frac{4 \pi \epsilon_0 a_0 m}{e}}$

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Ans: (c)

Sol: $\displaystyle \frac{m v^2}{a_0} = \frac{1}{4 \pi \epsilon_0}\frac{e^2}{a_0^2}$

$\displaystyle v^2 = \frac{1}{4 \pi \epsilon_0}\frac{e^2}{a_0 m}$

$\displaystyle v = \frac{e}{\sqrt{4 \pi \epsilon_0 a_0 m}}$