Question

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 and $e$ is 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. $\sqrt{\frac{4\pi\varepsilon_{0}a_{0}m}{e}}$

Answer 1

Answer: (C)

Centripetal force $=$ force of attraction of nucleus on electron
$\frac{m v^{2}}{a_{0}} =\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{e^{2}}{u_{0}^{2}}$
$v =\frac{e}{\sqrt{4 \pi \varepsilon_{0} m a_{0}}}$