Final answer:
To find the radius of curvature for a proton in a cyclotron, equate the magnetic force to the centripetal force and solve for the radius using the mass, charge, velocity of the proton, and the magnetic field strength.
Step-by-step explanation:
The radius of curvature of a charged particle like a proton moving in a magnetic field can be found by equating the magnetic force acting on the particle to the centripetal force required to keep the particle moving in a circular path. The formula for the radius of curvature (r) is given by:
r = mv/qB,
where:
- m is the mass of the proton,
- v is the velocity of the proton,
- q is the charge of the proton,
- B is the magnetic field strength.
To find v, we use the kinetic energy of the proton (25.0 MeV), and convert it to joules (J). The relation between kinetic energy (KE) and velocity (v) is:
KE = 1/2 mv^2
Solving for v gives:
v = (2KE/m)^1/2
After finding v, plug the values into the formula for r to compute the radius of curvature.