A proton, a deuteron and an alpha particle, are accelerated through the same potential difference and then subjected to a unifrom magnetic field `vecB`, perpendicular to the direction of their motions. Compare (i) their kinetic energies, and (ii) if the radius of the ciruclar path described by proton is 5 cm, determine the radii of the paths described by deuteron and alpha partcile.

Explanation

To solve the problem step by step, we will analyze the kinetic energies of the proton, deuteron, and alpha particle, and then calculate the radii of their circular paths in a magnetic field.

### Step 1: Determine the Kinetic Energies

When a charged particle is accelerated through a potential difference \( V \), its kinetic energy \( KE \) is given by:
\[ KE = QV \]
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