A proton and an $α$ -particle, accelerated through same potential difference, enter in a region of uniform magnetic field with their velocities perpendicular to the field. Compare the radii of circular paths followed by them.

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Solution

$α$ particle will be helium nucleus of
charge 2e and mass 4u
Proton will be hydrogen of
charge 1e and mass 1u
Radius of circle of charged particle in magnetic field will be
$r = \frac{m v}{q B}$
By Lorentz force,
Radius= $\frac{m o m e n t u m}{c h a r g e \times m a g n e t i c f i e l d}$
We know that radius is inversely proportional to charge
So Radius of alpha particle will be half of radius of proton
Hence ratio of Radii =1:2

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