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 $\varepsilon_{0}$ is the vacuum permittivity, the speed of the electron is
A) 0
B) $\frac{e}{\sqrt{\varepsilon_{0}a_{0}m}}$
C) $\frac{e}{\sqrt{4\pi\varepsilon_{0}a_{0}m}}$
D) $\frac{\sqrt{4\pi\varepsilon_{0}a_{0}m}}{e}$
Explanation
(c) $\frac{mv^{2}}{a_{0}} = \frac{1}{4\pi\varepsilon_{0}}\frac{e^{2}}{a_{0}^{2}} \Rightarrow v = \frac{e}{\sqrt{4\pi\varepsilon_{0}a_{0}m}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.