A proton (mass m and charge +e) and an $α$ -particle (mass 4m and charge +2e) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true?

Moderate

A

The $α - particle$ will be bent in a circular path with a smaller radius than that for the proton.
B

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

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

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

Solution

$r = \frac{\sqrt{2 mK}}{qB} i . e . r \propto \frac{\sqrt{m}}{q}$
Here kinetic energy K and magnetic field B are same.
$∴ \frac{r_{p}}{r_{α}} = \frac{\sqrt{m_{p}} q_{α}}{\sqrt{m_{α}} q_{p}} = \frac{\sqrt{m_{p}} 2 q_{α}}{\sqrt{4 m_{α}} q_{p}} = 1$

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