A proton, a deutron and `alpha`-particle, whose kinetic energies are same, enter perpendicularly a uniform magnetic field. Compare the radii of their circualr paths.

Explanation

To solve the problem of comparing the radii of the circular paths of a proton, a deuteron, and an alpha particle when they enter a uniform magnetic field perpendicularly with the same kinetic energy, we can follow these steps:

### Step 1: Understand the relationship between kinetic energy and velocity
The kinetic energy (K.E.) of a particle is given by the formula:
\[ K.E. = \frac{1}{2} mv^2 \]
where \(m\) is the mass of the particle and \(v\) is its velocity. Since the kinetic energies of the proton, deuteron, and alpha particle are the same, we can express their velocities in terms of their masses and the common kinetic energy \(K\).
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