Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic fields in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles. An α-particle and a photon are released from the centre of the cyclotron and made to accelerate: (i) Can both be accelerated at the same cyclotron frequency?

(a) Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. Inside the dees, the particle is acted upon only by magnetic field which makes it go round in a circular path. Every time the particle moves from one D to another it comes electric field acts upon it to increase it energy and its radius. Radius of the trajectory r = mv/qB Kinetic energy of ions = 1/2mv² = 1/2mr²q²B²/m ( ≈ rqB/m = v) (b)(i) Cyclotron frequency ν = Bq/2πm ν ∝ q/m For proton, νp ∝ q/m For alpha particle, να ∝ 2q/4m ∝ q/2m νp = 2να Particles will not accelerate with same cylotron frequency (ii) Velocity, v = Bqr/m For proton, vp ∝ q/m For alpha particle vα ∝ 2q/4m ∝ q/2m vp = 2vα Thus the particles will not leave the dees with same velocity.