Q. Mixed $He^{+}$ and $O^{2 +}$ ions (mass of ${He}^{+} = 4\ amu\ and\ that\ of\ O^{2 +} = 16\ amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then
A) $He^{+}\ $ions will be deflected more than those of $O^{2 +}$
B) $He^{+}$ ions will be deflected less than that of $O^{2 +}$
C) All the ions will be deflected equally
D) No ions will be deflected
Explanation
(c) $E = \frac{1}{2}mv^{2}$
or $v = \sqrt{\frac{2E}{m}}$
$q\ v\ B = \frac{mv^{2}}{r}$
or $r = \frac{mv}{qB} = \frac{m}{qB} \times \sqrt{\frac{2E}{m}} = \frac{\sqrt{2Em}}{qB}$
or $r \propto \frac{\sqrt{m}}{q}$
$\frac{r_{1}}{r_{2}} = \left( \frac{m_{He}}{m_{0}} \right)^{1/2} \times \left( \frac{q_{0}}{q_{He}} \right)$
$= \left( \frac{4}{16} \right)^{1/2} \times \left( \frac{2e}{e} \right) = 1$
$= r_{1} = r_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.