A proton and an α-particle (doubly ionised helium nucleus) are projected simultaneously with the same speed v at right angles to the same uniform magnetic field B.
(i) Derive expressions for the time periods T_p and T_α of their circular motions.
(ii) Show that the ratio T_p : T_α equals 1 : 2.
(iii) After how many complete revolutions of the proton will both particles again pass together through their common starting point?