Two electrons with kinetic energies K1 and K2 move in a uniform magnetic field, the lines of force of which

Two electrons with kinetic energies K1 and K2 move in a uniform magnetic field, the lines of force of which are perpendicular to the vectors of their velocities. Determine the ratio of the periods T1 / T2 of their motion along circular paths and the radii of curvature R1 / R2 of these paths.

ЕK = (m * V ^ 2) / 2 (kinetic energy);

V = √ ((2 * Eк) / m);
(m * V2) / R = e * B * V (1 case); m * V = e * B * R (2 case);

m * √ ((2 * Ek1) / m) = e * B * R1 (1 case);
m * √ ((2 * Eк2) / m) = e * B * R2 (2 case);
Let’s find the ratio of the first and second cases: R1 / R2 = √ (Ek1 / Ek2), because V = (2 * pi * R) / T, then:
T1 / T2 = ((2 * pi * R1) / V1) / ((2 * pi * R2) / V2) = (R1 * V2) / (R2 * V1) = Ek1 / Ek2.