In the Bohr's 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 and e is the charge on the electron, ε₀ is the vacuum permittivity, the speed of the electron is (a) zero (b) (e)/(√(ε₀ a₀ m)) (c) (e)/(√(4πε₀ a₀ m)) (d) (√(4πε₀ a₀ m))/(e)

Answer: (c). Centripetal force = Coulomb force: (mv²)/(a₀) = (e²)/(4πε₀ a₀²) v² = (e²)/(4πε₀ a₀ m) So the answer is (c) v = (e)/(√(4πε₀ a₀ m)).

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Bohr Model: Orbits, Speed & Angular Momentum

In the Bohr's 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 electron, $\varepsilon_0$ is the vacuum permittivity, the speed of the electron is

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Answer: (c)

Centripetal force = Coulomb force: $\frac{mv^2}{a_0} = \frac{e^2}{4\pi\varepsilon_0 a_0^2}$
$v^2 = \frac{e^2}{4\pi\varepsilon_0 a_0 m}$
So the answer is (c) $v = \frac{e}{\sqrt{4\pi\varepsilon_0 a_0 m}}$ .

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