Question

In a Bohr model of an atom, find the centripetal acceleration.

A) e² / (4 * π * ε₀ * r²)
B) e² / (2 * π * ε₀ * r²)
C) (2 * e²) / (4 * π * ε₀ * r²)
D) e² / (π * ε₀ * r²)

Answer 1

In the Bohr model of an atom, the centripetal acceleration is given by e² / (4πε0r²), corresponding to option A.

Step-by-step explanation:

Within the context of a Bohr model of an atom, the centripetal acceleration is provided by the Coulomb force due to the electrostatic attraction between the positively charged nucleus and the negatively charged electron. The centripetal force, which is necessary to keep the electron in a circular orbit, is given by the expression Fc = mv²/r, where m is the mass of the electron, v is its velocity, and r is the radius of the orbit. Concurrently, the Coulomb force is expressed as Fc = k(Ze)(-e)/r², where k is Coulomb's constant, Z is the atomic number, and e is the elementary charge. Equating the two expressions for force and solving for acceleration yields ac = e² / (4πε0r²), which matches option A.