The diameter of the largest orbit is:

$\overline{){\mathbf{d}}{\mathbf{=}}{\mathbf{2}}{\mathbf{r}}}$, where r is the radius of the orbit.

The radius, r, of the orbit is:

$\overline{){\mathbf{r}}{\mathbf{=}}\frac{\mathbf{m}\mathbf{v}}{\mathbf{B}\mathbf{q}}}$, where m is the mass of protons, v is the velocity of the proton, B is the magnetic field, and q is the charge of the proton.

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Therefore,

$\overline{){\mathbf{d}}{\mathbf{=}}\frac{\mathbf{2}\mathbf{m}\mathbf{v}}{\mathbf{B}\mathbf{q}}}$

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.2 T.

a. What is the diameter of the largest orbit, just before the protons exit the cyclotron?

b. A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Nuclear Physics concept. You can view video lessons to learn Nuclear Physics. Or if you need more Nuclear Physics practice, you can also practice Nuclear Physics practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Krishna & Avery & Weatherford's class at UF.