Q. A cyclotron is used to accelerate protons, deuterons $\alpha - \ $particle etc. If the energy attained, after acceleration, by the protons is $E$, the energy attained by $\alpha -$ particles shall be
A) 4 $E$
B) 2$E$
C) $E$
D) $E/4$
Explanation
(c) Kinetic energy of the ions,
$\frac{1}{2}mv^{2} = \frac{q^{2}B^{2}R^{2}}{2m}$
For $\alpha$ particle, the charge is two times that of the proton but mass is 4 times that of the proton
Therefore, compared to proton’ kinetic energy, for the same conditions in the cyclotron, energy of alpha particle is $E$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.