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since the period fo revolution of electronsin a unifrommagnetic fieldrapidlyincreaseswith the growthof energy, acyclotron in unsuitable for theiraccelearation. Thisdrawbackis rectifiedin a microton(Fig) in which a changeDelta Tin theperiod of revolutionof an electronis made multipilewith theperiodof accleratingfield T_(0). How many timeshas anelectronto crossthe acceratinggap of a microtronto acquirean energyW = 4.6 MeV if DeltaT = T_(0) the magneticinduction is equalto B = 107 mT, andthe frequency of accelerating field tov = 3000 MHz ? |
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Answer» Solution :In the nth oribit, `(2pi r_(n))/(v_(n)) = n T_(0) = (n)/(v)`. We igonre the rest mass of the electronand write `v_(n) = c`. Also `W = cp = cBer_(n)`. THUS, `(2pi W)/(B EC^(2)) = (n)/(v)` or, `n = (2pi W v)/(Be c^(2)) = 9` |
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