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A proton and an $α -$ particle are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true.

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The $α -$ particle will bent in a circular path with a small radius than that for the proton

The radius of the path of the $α -$ particle will be greater than that of the proton

The $α -$ particle and the proton will be bent in a circular path with the same radius

The $α -$ particle and the proton will go through the field in a straight line

answer is C.

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Detailed Solution

$r = \frac{m v}{q B} = \frac{\sqrt{2 m K}}{q B}$

$r \propto \frac{\sqrt{m}}{q}$

$\frac{r_{p}}{r_{α}} = (\sqrt{\frac{m}{4 m}}) \times (\frac{2 e}{e}) = 1$

The $α -$ particle and the proton will be bent in a circular path with the same radius.

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