A proton and an alpha particle of the same velocity enter in a...

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is

Options

A $4: 1$
B $2: 1$
C $1: 2$
D $1: 4$

Correct answer

B. $2: 1$

Step-by-step solution

Radius of circular path of charged particle $\left(q\right)$ of mass $\left(m\right)$ moving with velocity $\left(v\right)$ in magnetic field $\left(B\right)$ is given by $r = \dfrac{mv}{qB}$

$\dfrac{{r}_{\alpha}}{{r}_{p}} = \dfrac{\dfrac{\left(4m\right)v}{\left(2e\right)B}}{\dfrac{mv}{eB}} = 2: 1$

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