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A proton, a deuteron and an $α$ -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 :

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$1 : \sqrt{2} : \sqrt{2}$

$\sqrt{2} : 1 : 1$

$1 : 1 : \sqrt{2}$

$1 : \sqrt{2} : 1$

answer is D.

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Detailed Solution

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

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