Question

A cyclotron accelerates deuterons to $16MeV$ energy. lf deuterium is replaced by helium what will be the energy of alpha particles?

• A. $32MeV$
• B. $8MeV$
• C. $24MeV$
• D. $48MeV$

Answer 1

The correct option is A $32MeV$

Mass of deutrium = $\frac{1}{2}$ mass of helium
$V=\frac{qBr}{m}$
$V\alpha \frac{q}{m}$
$2m=m_{He}$ , $2q_D=q_{He}$
$\therefore V_D=V_{He}$
$\therefore 16=\frac{1}{2}{m}_D{V}_D^2$
$KEofHe=\frac{m_{He}}{2}{V}_{He}^2$
$=\frac{2}{2}{m}_D{V}_D^2=2\left(16\right)MeV$
therefore KE of particle is $32MeV$.