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A cyclotron's oscillator frequency is 10...

A cyclotron's oscillator frequency is 10 MHz. What should be the opertaing magnetic field for accelerating protons ? If the radius of its 'dees' is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator.
`(e=1.60xx10^(-19)C, m_(p)=1.67xx10^(-27)kg, 1 MeV = 1.6xx10^(-13) J)`.

Text Solution

Verified by Experts

The oscillator frequency should be same as proton.s cyclotron frequency.
Using equations `r= mv/ qB` and `omega = 2piv = qB/ m `we have `B=2 pi mv/q = 6.3xx1.67xx10^(-27) xx10^(7)/(1.6 xx10^(-19))`=0.66T
Fint velocity of protons is
`v=r xx2piv=0.6mxx6.3xx10^(7)=3.78xx10^(7)=3.78xx10^(7)m//s`
`E=1/2 mv^(2)=1.67xx10^(-27)xx14.3xx10^(14)/(2xx1.6xx10^(-13))=7 MeV`
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