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 the charge on the election and ${\epsilon }_0$ 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. $\sqrt{\frac{4\pi {\epsilon }_0{a}_{0}m}{e}}$

Answer 1

Answer: (C)

$\frac{e}{\sqrt{4\pi {\epsilon }_0{a}_{0}m}}$

Centripetal force$=\frac{m{v}^2}{a_{\circ }}\to \left(1\right)$

Colounbic force$=\frac{1}{4\pi {\epsilon }_{\circ }}\frac{e.e}{a^2}\to \left(2\right)$

$\therefore$ Centripetal force= Coloumbic force

$\to \frac{m{v}^2}{a_{\circ }}\frac{1}{4\pi {\epsilon }_{\circ }}\frac{e^2}{{a_{\circ }}^2}\to v^2=\frac{e^2}{4\pi {\epsilon }_{\circ }{a}_{\circ }m}orv=\frac{e}{\sqrt{4\pi {\epsilon }_{\circ }{a}_{\circ }m}}$