(a)

The magnetic force acts as centripetal force, so we can write

where
q is the charge of the particle
v is its speed
B is the magnetic field strength
m is the mass
r is the radius of the circular path
For the alpha particle in the problem,



B = 1.17 T
Re-arranging the equation and solving for v, we find its speed:

(b)

The period of revolution is given by the ratio between the distance travelled in one circle (so, the circumference of the path) and the speed of the particle, so

where
r is the radius of the path
v is the speed
Here we have


So the period of revolution is

(c)

The kinetic energy of a particle is given by

where
m is its mass
v is its speed
For the alpha particle in the problem, we have


So its kinetic energy is

(d)

When accelerated through a potential difference, a particle gains a kinetic energy equal to the change in electric potential energy - so we can write:

where the term on the left is the change in electric potential energy, with
q is the charge of the particle
is the potential difference
Here we have
is the charge of the alpha particle
is the kinetic energy
Re-arranging the formula, we find
