The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the lowest energy orbit the distance from the proton to the electron is 5.29 x 10-11 m, and the linear speed of the electron is 2.18 x 106 m/s. How many orbits about the proton does it make each second

a) The angular velocity of the electron is

b) The number of revolutions per second is rev/s

c) The centripetal acceleration of the electron is

Explanation:

a)

This is a problem of uniform circular motion: in fact, the electron orbits around the proton in a uniform circular motion.

The angular velocity of an object in uniform circular motion is given by

where

v is the linear speed

r is the radius of the trajectory

For the electron orbiting around the proton, we have

Therefore, the angular velocity is

b)

The period of revolution of the electron is given by

where

is the angular velocity

Substituting,

The period is the time the electron takes to make one complete orbit around the proton; therefore, the number of revolutions of the electrons in one second is:

rev/s

c)

The centripetal acceleration of an object in circular motion is

where

v is the linear speed

r is the radius of the circle

For the electron, we have

Therefore, the centripetal acceleration is

Learn more about circular motion:

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