Introduction:
When a charged particle moves in a magnetic field, it experiences a force known as the magnetic Lorentz force. This force acts perpendicular to both the velocity of the particle and the magnetic field. In a circular orbit, the magnetic force is balanced by the centripetal force, resulting in a stable path.

Determining the Energy of the Alpha Particle:
To determine the energy of the alpha particle required for it to revolve in a circular orbit, we need to consider the balance between the magnetic force and the centripetal force.

Centripetal Force:
The centripetal force acting on the alpha particle is provided by the electrostatic force. In a circular orbit, the centripetal force is given by the equation:
F_c = mv^2/r
where F_c is the centripetal force, m is the mass of the alpha particle, v is its velocity, and r is the radius of the orbit.

Magnetic Force:
The magnetic force acting on the alpha particle is given by the equation:
F_m = qvB
where F_m is the magnetic force, q is the charge of the alpha particle, v is its velocity, and B is the magnetic field strength.

Equating the Forces:
For the alpha particle to remain in a circular orbit, the magnetic force must be equal to the centripetal force. Therefore, we can equate the two equations:
mv^2/r = qvB

Calculating the Energy:
The energy of the alpha particle can be calculated using the equation:
E = (1/2)mv^2

Rearranging the Equations:
By rearranging the equation for the magnetic force, we can express v in terms of r, B, and q:
v = (qBr)/m

Substituting this expression for v into the equation for energy, we get:
E = (1/2)m((qBr)/m)^2
E = (1/2)(q^2Br^2)/m

Conclusion:
The energy of the alpha particle required for it to revolve in a circular orbit can be calculated using the equation E = (1/2)(q^2Br^2)/m. By knowing the mass and charge of the alpha particle, the strength of the magnetic field, and the radius of the orbit, we can determine the energy needed. This energy ensures that the magnetic force acting on the alpha particle is balanced by the centripetal force, allowing it to maintain a stable circular path.