Q. An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_{e},\ R_{p},\ R_{d}$ and $R_{\alpha}.$ If follows that
A) $R_{e} = R_{p}$
B) $R_{p} = R_{d}$
C) $R_{d} = R_{\alpha}$
D) $R_{p} = R_{\alpha}$
Explanation
(c) In perpendicular magnetic field magnetic force = centripetal force.
$\therefore$ By the relation
$qvB = \frac{mv^{2}}{r}$
$\Rightarrow \ \ r = \frac{mv}{qB} \Rightarrow \ r \propto \frac{m}{q}$
Since, $\frac{m}{q}$ ratio for deuteron and $\alpha$-particle is same.
$\left( \frac{m}{q} = \frac{4}{2} = 2\ for\ \ \alpha - particle \right)\ and\ \frac{m}{q} = \frac{2}{1} = 2$ for deuteron.
Hence, radius is same for both.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.