# Problem: 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?

###### FREE Expert Solution

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,

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

85% (493 ratings)
###### Problem Details

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?