A proton, a deuteron and an α -particle with same kinetic energy...

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 :

Options

A $1: \sqrt{2}: \sqrt{2}$
B $1: \sqrt{2}: 1$
C $\sqrt{2}: 1: 1$
DNone of these

Correct answer

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

Step-by-step solution

Radius of circular path in magnetic field is given by

$R = \dfrac{mv}{qB} = \dfrac{m\left(\sqrt{2\left(KE\right)}\right)}{qB\sqrt{m}} ∝ \dfrac{\sqrt{m}}{q}$

${R}_{P}: {R}_{D}: {R}_{\alpha} = \dfrac{1}{1}: \dfrac{\sqrt{2}}{1}: \dfrac{\sqrt{4}}{2} = 1: \sqrt{2}: 1$

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