Q. A proton, a deuteron and an alpha particle with the same kinetic energy enter a region of uniform magnetic field $B$ at right angles to the field. The ratio of the radii of their circular paths is
A) 1 : 1 : 1
B) $1\ :\ \sqrt{2}\ :\sqrt{2}$
C) $\sqrt{2}\ :1\ :1$
D) $\sqrt{2}\ :\sqrt{2}\ :1$
Explanation
(b) Radius of circular paths is proportional to square root of mass,
$R \propto \sqrt{m}$
$\frac{R_{d}}{R_{p}} = \ \sqrt{\frac{m_{d}}{m_{p}}} = \frac{\sqrt{2}}{1}$
$\Rightarrow \frac{R_{p}}{R_{d}} = \frac{1}{\sqrt{2}}$
Also, $\frac{R_{d}}{R_{\alpha}} = \frac{\sqrt{M_{d}}}{\sqrt{M_{\alpha}}} = \frac{\sqrt{2}}{\sqrt{4}} = \frac{1}{\sqrt{2}}$
Hence, ratio is $1\ :\ \sqrt{2}\ :\sqrt{2}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.