Question

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.6 T .

Part A

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

Express your answer with the appropriate units.

d =

3mm

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Enter your answer using dimensions of distance.

Part 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?

N =

orbits

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Answer 1

kinetic energy, K = 6.5 MeV = 6.510⁶1.610^-19 J = 10.410^-13 J

mass of proton,m = 1.6710^-27kg,   velocity = v, Then, K =0.5mv²

v = 3.52910⁷ m/s

radius,

B = 1.6 T, q = 1.610^-19C

r = 0.2302 m

Diameter = 2r = 0.4604 m

B)

N = 24398