In the Bohr model of the hydrogen atom, the electron...

In the Bohr model of the hydrogen atom, the electron revolves in a circular orbit around the nucleus. If the radius is $5.3 \times 10^{-11} \mathrm{~m}$ and the electron makes $6.6 \times 10^{15} \mathrm{rev} / \mathrm{s}$, find (a) the speed of the electron, $(b)$ the acceleration of the electron, and $(c)$ the force acting on the electron. (This force is the result of the attraction between the positively charged nucleus and the negatively charged electron.)

In the Bohr model of the hydrogen atom, the electron revolves in a circular orbit around the nucleus. If the radius is $5.3 \times 10^{-11} \mathrm{~m}$ and the electron makes $6.6 \times 10^{15} \mathrm{rev} / \mathrm{s}$, find
(a) the speed of the electron, $(b)$ the acceleration of the electron, and $(c)$ the force acting on the electron. (This force is the result of the attraction between the positively charged nucleus and the negatively charged electron.)

Key Concepts

Bohr Model

The Bohr model describes the hydrogen atom as having an electron that moves in a circular orbit around a nucleus due to electrostatic attraction. It introduces the idea of quantized electron orbits, where only specific allowed distances from the nucleus correspond to stable electron motion.

Circular Motion

Circular motion refers to the movement of an object along a circular path. In this context, the electron in a hydrogen atom moves along a circular orbit, which implies that while its speed might be constant, its velocity is continually changing due to its continuously changing direction.

Centripetal Acceleration

Centripetal acceleration is the inward acceleration required to keep an object moving in a circle, mathematically defined as the square of the speed divided by the radius of the circle. This concept is fundamental in explaining how the electron remains in a circular orbit despite having a constant speed.

Centripetal Force

Centripetal force is the net force that acts on an object moving in a circular path, directed towards the center of the circle. In the case of the hydrogen atom, this force is provided by the electrostatic attraction between the positively charged nucleus and the negatively charged electron.

Coulomb's Law

Coulomb's law quantifies the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, and this law underpins the interaction that provides the centripetal force in the hydrogen atom.

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