Question

Cyclotron is used to accelerate charged particles in a limited space. The maximum energy of a deuteron coming out of a cyclotron accelerator is $20MeV$ . The maximum energy of protons that can be obtained from this accelerator is

• A. $10MeV$
• B. $20MeV$
• C. $30MeV$
• D. $40MeV$

Answer 1

Answer: (D)

$R=\frac{mV}{BQ}$
$\therefore KE=\frac{1}{2}m{V}^2=\frac{1}{2}m{\left(\frac{BQR}{m}\right)}^2=\frac{B^2{Q}^2{R}^2}{2m}$
$\therefore KE\propto \frac{Q^2}{m}$
$\therefore \frac{K_1}{K_2}={\left(\frac{Q_1}{Q_2}\right)}^2\cdot \left(\frac{m_2}{m_1}\right)={\left(\frac{1}{1}\right)}^2\cdot \left(\frac{1}{2}\right)$
$\therefore K_2=40MeV$ .