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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