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Protons are acceleratedin a cyclotronso that the maximum curvatureradiusof theirtrajectoryis equalto r = 50 cm. Find: (a) the kinetic energyof the protonswhen the acceleration is completedif the magnetic induction in the cyclotron is B= 1.0 T, (b) the minimum frequencyof the cycloroton'soscillator at whichthe kinetic energyof theprotons amountsto T = 20 Me V by theend of accelearation. |
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Answer» SOLUTION :(a) From `(mv^(2))/(R) = Bev`, or, `mv = BER` and`T = ((Ber)^(2))/(2m) = (1)/(2) mv^(2) = 12 MeV` (b) From `(2pi)/(omega) = (2pi r)/(v)` we get, `f_(min) = (v)/(2pi r) = (1)/(pi r) sqrt((T)/(2m)) = 15 MHz` |
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