Question

A proton (mass m and charge +e) and an $\alpha -$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

• A. The $\alpha -$particle will be bent in a circular path with a small radius that for the proton
• B. The radius of the path of the $\alpha -$particle will be greater than that of the proton
• C. The $\alpha -$particle and the proton will be bent in a circular path with the same radius
• D. The $\alpha -$particle and the proton will go through the field in a straight line

Answer 1

Answer: (C)

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

Answer 2

$r = \frac { \sqrt { 2 m K } } { q B }$ i.e. $r \propto \frac { \sqrt { m } } { q }$

Here kinetic energy K and B are same.

$\therefore \frac { r _ { p } } { r _ { \alpha } } = \frac { \sqrt { m _ { p } } } { \sqrt { m _ { \alpha } } } \cdot \frac { q _ { \alpha } } { q _ { p } } = \frac { \sqrt { m _ { p } } } { \sqrt { 4 m _ { p } } } \cdot \frac { 2 q _ { p } } { q _ { p } } = 1$