(i) Derivation of the expression for cyclotron frequency (ii) Reason / justification for the correct answer2 (i) Suppose the positive charge ion with charge $q$ moves in a circle with a velocity $v$,then: $\; \frac{m v^2}{r} \; = q v B$ $r \; = \; \frac{m v}{q B}$ Frequency of revolution $\; f = \; \frac{1}{\; \text{ Time Period }\; } = \; \frac{v}{2 \pi r}$ $\; f = \; \frac{q B}{2 \neq m}$ (ii) No The masses of the two particles, i.e. deuteron and proton, are different. Since (cyclotron) frequency depends inversely on the mass, they cannot be accelerated by the same oscillator frequency.