Explanation:

Given:
Mass of proton (mp) = 1847 times mass of electron (me)
Initial kinetic energy (KE) of both particles is the same.

To understand the trajectories of the proton and electron in a uniform electric field, we need to consider the motion of charged particles in an electric field.

Motion of Charged Particles in an Electric Field:
When a charged particle is placed in an electric field, it experiences a force given by the equation: F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength.

The force experienced by a charged particle causes it to accelerate, and the resulting motion can be analyzed using Newton's second law: F = ma, where m is the mass of the particle and a is the acceleration.

Differentiating Trajectories of Proton and Electron:
Since the initial kinetic energy of both particles is the same, we can assume that their initial velocities are also the same. However, due to the difference in their masses, their accelerations will be different.

- Proton:
The mass of the proton is larger than that of the electron, so its acceleration will be smaller for the same force. As a result, the proton will have a smaller acceleration and a larger radius of curvature compared to the electron.

- Electron:
The mass of the electron is smaller than that of the proton, so its acceleration will be larger for the same force. As a result, the electron will have a larger acceleration and a smaller radius of curvature compared to the proton.

Conclusion:
In summary, when both the proton and electron are injected into a uniform electric field at right angles to the field direction, the proton will have a larger radius of curvature and a smaller acceleration compared to the electron. This difference in trajectories is due to the difference in their masses.