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)

$R=\frac{m V}{B Q}$
$\therefore KE=\frac{1}{2}mV^{2}=\frac{1}{2}m\left(\frac{B Q R}{m}\right)^{2}=\frac{B^{2} Q^{2} R^{2}}{2 m}$
$\therefore KE \propto \frac{Q^{2}}{m}$
$\therefore \frac{K_{1}}{K_{2}}=\left(\frac{Q_{1}}{Q_{2}}\right)^{2}\cdot \left(\frac{m_{2}}{m_{1}}\right)=\left(\frac{1}{1}\right)^{2}\cdot \left(\frac{1}{2}\right)$
$\therefore K_{2}=40MeV$ .