Answer :
The frequency of revolution of an electron with an energy of 100 ev in a uniform magnetic field of magnitude 35.0 mt is 9.78 x 10^5 Hz
What is cyclotron frequency?
A charged particle travelling perpendicular to the direction of an even magnetic field has a frequency that is known as the cyclotron frequency or gyrofrequency (constant magnitude and direction). The cyclotron frequency is determined by the centripetal force and magnetic Lorentz force being equal because that motion is always circular.
Kinetic Energy of the electron = 100 ev
= 100×(1.60×10^−19 J)
= 1.60×10 ^−17 J
The expression of kinetic energy of the electron in terms of the velocity-
E = mv^2/2
v = (2E/m)^1/2
Putting the values in the above expression we obtain the value of v,
v = ( 2 x 1.60 x 10 ^−17/ 9.1 x 10^-31)^1/2
= 5.92 x 10^6 m/s
The radius of the circular path the electron moves inside a magnetic field is given as-
r = mv / eB
Putting the values we find,
r = (9.11×10^−31 kg)(5.92×10^6m/s)/ (1.6 x 10^-19 C)(35 x 10^-6 T)
= 0.963 m
The orbital frequency is same as the velocity of the electron when it moves over the circular path, which is given as-
f = v / 2πr
= (5.92×10^6 m/s)/2π(0.963 m)
= 9.78 x 10^5 Hz
Hence, the required frequency is 9.78 x 10^5 Hz
To learn more about cyclotron frequency from the given link
https://brainly.com/question/12946099
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