The Bohr model of the hydrogen atom proposes that the...

The Bohr model of the hydrogen atom proposes that the electron orbits around the proton in a circle of radius $5.3 \times 10^{-11} \mathrm{~m}$. The electric force is responsible for the radial acceleration of the electron. What is the speed of the electron in this model?

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Key Concepts

Coulomb Force

Coulomb's law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In the context of the hydrogen atom, this law is used to calculate the electric force acting on the electron due to the proton.

Centripetal Force and Circular Motion

For an object moving in a circular path, a centripetal force must act inward to keep it in that path. In the case of the hydrogen atom in the Bohr model, the necessary centripetal force to maintain the electron’s circular orbit is provided by the Coulomb force between the electron and the proton. Equating these forces allows one to deduce the electron's orbital speed.

Bohr Model

The Bohr model is an early atomic theory that describes electrons orbiting the nucleus in fixed, quantized circular orbits. It proposes that the electron's orbit has a defined radius and that the centripetal force required for its circular motion is provided by the electrostatic (Coulomb) attraction between the negatively charged electron and the positively charged nucleus.

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