A proton, a deuteron and an α -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 t

Question

A proton, a deuteron and an α -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

TestHub · Accepted Answer

According to the question, magnetic field is uniform and the kinetic energy for each particle is same.

We know that,

$r = \frac{m v}{q B} = \frac{\sqrt{2 m (K . E.)}}{q B}$

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

$r_{p} : r_{d} : r_{α} = \frac{\sqrt{1}}{1} : \frac{\sqrt{2}}{1} : \frac{\sqrt{4}}{2}$

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

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