Which on the following will describe the smallest circle when projected with the same velocity v perpendicular to the magnetic field B: (i)`alpha` -particle (ii) `beta`-particle?

Explanation

To determine which particle will describe the smallest circle when projected with the same velocity \( v \) perpendicular to a magnetic field \( B \), we need to analyze the relationship between the radius of the circular path, the mass, and the charge of the particles involved.

### Step-by-Step Solution:

1. **Understanding the Motion in a Magnetic Field:**
When a charged particle moves in a magnetic field perpendicular to its velocity, it experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path. The radius \( r \) of this circular path is given by the formula:
\[
r = \frac{mv}{qB}
...