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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 ε₀ is the vacuum permittivity, the speed of the electron is

1. 0
2. √e²a₀m
3. e / √4πε₀a₀m
4. √4πε₀a₀m / e

Correct answer: e / √4πε₀a₀m

Solution

In the Bohr model, the centripetal force is provided by the Coulomb force: (mv²)/a₀ = (e²)/(4πε₀a₀²). Solving for v, we get v = e / √(4πε₀a₀m).

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