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 a₀ is the radius of the ground state orbit, m is the mass e is the charge on the electron and e₀ 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. $\frac{\sqrt{4\pi\varepsilon_{0}a_{0}m}}{e}$

Answer 1

Answer: (C)

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

Answer 2

$\frac{mv^{2}}{r}$ =$\frac{(e)(e)}{4\pi\varepsilon_{0}r^{2}}$ or v = $\sqrt{\frac{e^{2}}{4\pi\varepsilon_{0}mr}}$