Solution

The magnetic force provides the centripetal force: $evB = \dfrac{mv^2}{r} \Rightarrow r = \dfrac{mv}{eB}$
Time period: $T = \dfrac{2\pi r}{v} = \dfrac{2\pi m}{eB}$
Frequency: $f = \dfrac{1}{T} = \dfrac{eB}{2\pi m}$
The frequency does not depend on the speed or kinetic energy E of the electron; only the radius does.
(The expression $\dfrac{2\pi m}{eB}$ is the time period, not the frequency.)

Concept Frequency independent of speed

Moving Charges and Magnetism in past papers

89 questions from this chapter have appeared across 27 exam years.