(i) Derivation of the expression for cyclotron frequency
(ii) Reason / justification for the correct answer2
(i) Suppose the positive charge ion with charge $\mathit{q}$ moves in a circle with a velocity $\mathit{v}$,then:
$\frac{\mathit{m}{\mathit{v}}^2}{\mathit{r}}=\mathit{q}\mathit{v}\mathit{B}$
$\mathit{r}=\frac{\mathit{m}\mathit{v}}{\mathit{q}\mathit{B}}$
Frequency of revolution

$\mathit{f}=\frac{\mathit{q}\mathit{B}}{2\ne \mathit{m}}$
(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.