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 a0 is the radius of the ground state orbit m is the mass, e is the charge on the electron and ε0 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: $\displaystyle \frac{m v^2}{a_0} = \frac{1}{4 \pi \epsilon_0}\frac{e^2}{a_0^2}$
$\displaystyle v^2 = \frac{1}{4 \pi \epsilon_0}\frac{e^2}{a_0 m}$
$\displaystyle v = \frac{e}{\sqrt{4 \pi \epsilon_0 a_0 m}}$