Two electrons, e 1 and e 2 of mass m and charge q are injected into the perpendicular direction of the…

As elocity of particles are perpendicular to the magnetic field, thus the particles moves in a circle.

The centripetal force is experienced by electron is $qvB$.

So, $\frac{m{v}^2}{r}=qvB$

 $$\begin{gathered} \Rightarrow \frac{mv}{r}=qB \\ \Rightarrow m\omega =qB\Rightarrow \omega =\frac{qB}{m} \end{gathered}$$

Frequency is given by $f=\frac{qB}{2\pi m}$.

As frequency is independent of kinetic energy, so $f_1=f_2$.