Question

in a cyclotron , for the same B and R, show tat the maximum kinetic energy of a particles is twice that of deuterons

Answer 1

Dear student,

In a cyclotron, a charge particle follows the equation,
$$\begin{gathered} \frac{m{v}^2}{r}=qvB \\ \mathrm{Multiplying}\mathrm{by}\frac{r}{2}\mathrm{on}\mathrm{both}\mathrm{side},\mathrm{we}\mathrm{get} \\ \frac{m{v}^2}{2}=\frac{rqvB}{2} \\ \Rightarrow KE=\frac{rqvB}{2} \end{gathered}$$
For same B and r,
$KE\propto q$
ie, a particle having charge equal to double of deuteron will have kinetic energy twice that of deuteron.

Regards.