Question

A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

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

Answer 1

Answer: (D)

$R=\frac{\sqrt{2km}}{qB}\propto \frac{\sqrt{m}}{q}$
$\frac{\sqrt{m}}{e}:\frac{\sqrt{2m}}{e}:\frac{\sqrt{4m}}{2e}$
$1:\sqrt{2}:1$