Please help me with my homework. There are three parts tothis question I hope yo

Question

Please help me with my homework. There are three parts tothis question I hope you don't mind helping me. even if yousolve only one part I will be grateful. 17-64 A cyclotron with a magnetic field B=0.9T and a maximum orbitalradius of 50 cm is used to accelerate deuterons (2Hnuclei). (A) What is the maximum energy to which the deuterons can beaccelerated? (B) What should be the frequency of the AC acceleratingvoltage? (C) If the accelerating voltage has amplitude 40 kV, how manyrevolutions are needed to bring the deuterons to fullenergy?
Answer is 121 or 60.5 depends on interpretation ( teacher gave usthis answer) Please help me with my homework. There are three parts tothis question I hope you don't mind helping me. even if yousolve only one part I will be grateful. 17-64 (A) What is the maximum energy to which the deuterons can beaccelerated? (B) What should be the frequency of the AC acceleratingvoltage? (C) If the accelerating voltage has amplitude 40 kV, how manyrevolutions are needed to bring the deuterons to fullenergy?
Answer is 121 or 60.5 depends on interpretation ( teacher gave usthis answer)

Explanation / Answer

(A) For the maximum orbital radius R, Centripetal force necessary for containing the deuteron, Fc = m*v*v/R = qvB So, v = qBR/m So, KEmax = mv2/2 = m(qBR/m)2/2 = q2B2R2/2m =............... (B) The AC frequency should be such that by the time thedeuterons complete half the revolution in the cyclotron, the polarity of the voltage reverses once. So, the frequencyof AC should be equal to 1/T of the deuteron revolution. Now, T = 2/ m2r = qvB = qrB => T = 2/(qB/m) = 2m/qB So, f = 1/T = qB/2m = ........... (C) The accelerating voltage adds q*V energy to the deuteronsin each revolution.        So,q2B2R2/2m = N*q*V        => N =qB2R2/2mV = ...............

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