Question

A proton, a deuteron and an $\alpha $ -particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energies. The ratio of the radii of the circular paths described by them is

• A. $1:\sqrt{2}:1$
• B. $1:\sqrt{2}:\sqrt{2}$
• C. $\sqrt{2}:\sqrt{2}:1$
• D. $\sqrt{2}:1:1$

Answer 1

Answer: (A)

According to the question, magnetic field is uniform and the kinetic energy for each particle is same.
We know that,
$r=\frac{m v}{q B}=\frac{\sqrt{2 m \left(K . E.\right)}}{q B}$
$r \propto \frac{\sqrt{m}}{q}$
$r_{p}:r_{d}:r_{\alpha }=\frac{\sqrt{1}}{1} : \frac{\sqrt{2}}{1} : \frac{\sqrt{4}}{2}$
$=1:\sqrt{2}:1$