Question

In a cyclotron, for the same B and R, show that the maximum kinetic energy of α-particles is twice that of deuterons.

Answer 1

Data: Let E_α and E_d denote the maximum kinetic energies of α-particIes (He⁺⁺ ions) and deuterons

(D⁺ ions). For an α-partic1e,

q = +2e and m ≅ 4m^p and for a deuteron, 

q = +e and m ≅ 2m^p

where e is the elementary charge and m^p is the proton mass.

In a cyclotron, the maximum kinetic energy of the ions obtainable with dec radius R and magnetic field induction B is