How Long Does It Take for Alpha Particles to Complete One Orbit in a Cyclotron?

[eaw07]

Homework Statement

Alpha particles (charge= +2e, mass= 6.68*10^-27kg) are acclerated in a cyclotron to a final orbit radius of .30 m. THe magnetic field in the cyclotron is .80 T. The period of circular motion is?

Homework Equations

f=1/T
F=qvbsin$$\alpha$$
There might be more!

The Attempt at a Solution

 

[LowlyPion]

Welcome to PF.

Don't you want to consider the effect of centripetal acceleration?

Won't mv²/R = qv X B yield your velocity and from that you can figure how long to make 1 revolution?

 

[nlightner]

The period of circular motion of the alpha particles can be calculated using the equation T=2πr/v, where r is the orbit radius and v is the velocity of the particle. In this case, the velocity can be found using the equation F=qvb, where q is the charge of the particle, v is the velocity, and b is the magnetic field.

Substituting the given values, we have:

v = F/qb = (2*1.6*10^-19 C)(.80 T)/ (6.68*10^-27 kg)(.30 m) = 3.81*10^6 m/s

Therefore, the period of circular motion is:

T = 2π(.30 m)/(3.81*10^6 m/s) = 5.23*10^-8 seconds

This means that the alpha particles complete one full orbit in approximately 52.3 nanoseconds.