Introduction:
When a charged particle moves in a uniform magnetic field, it experiences a force perpendicular to its velocity. Due to this force, the particle moves in a circular path called a cyclotron orbit. The energy of the particle is related to its velocity and mass. In this case, we are given the energy of a proton and need to determine the energy of an alpha particle moving in the same magnetic field and along the same path.

Given:
Energy of proton (E) = 8 eV

Explanation:
To find the energy of an alpha particle, we first need to understand the relation between energy, velocity, and mass of a charged particle.

1. Energy of a charged particle:
The energy (E) of a charged particle can be calculated using the equation:
E = (1/2)mv^2
where m is the mass of the particle and v is its velocity.

2. Relation between velocity and energy:
We can rearrange the equation for energy to solve for velocity:
v = √(2E/m)
This equation shows that the velocity of a particle is directly proportional to the square root of its energy and inversely proportional to the square root of its mass.

3. Mass of a proton and an alpha particle:
A proton and an alpha particle have different masses. The mass of a proton is approximately 1.67 x 10^-27 kg, while the mass of an alpha particle is approximately 6.64 x 10^-27 kg. Therefore, the mass of an alpha particle is four times greater than that of a proton.

4. Relation between velocities of proton and alpha particle:
Using the equation for velocity, we can observe that the velocity of a particle is inversely proportional to the square root of its mass. Since the mass of an alpha particle is four times greater than that of a proton, the velocity of the alpha particle will be half that of the proton.

5. Relation between energies of proton and alpha particle:
Since the energy of a particle is directly proportional to the square of its velocity, the energy of the alpha particle will be one-fourth (1/2)^2 = 1/4 of the energy of the proton.

Conclusion:
Therefore, the energy of the alpha particle moving in the same magnetic field and along the same path will be one-fourth (1/4) of the energy of the proton, given that the energy of the proton is 8 eV. Hence, the energy of the alpha particle will be 2 eV.