A cyclotron is used to acclerate protons to a kinetic energy of 5 MeV. If the radius and the frequency field in the cyclotron is 2T. Find the radius and the frequency needed for the applied alternating voltage of the cyclotron. (Given : Velocity of proton `=3xx10^(7)m//s)`

Explanation

Given `K.E=5MeV`
Magnetic field, `B=2T`
Velocity of proton `(v) =3xx10^(7)m//s`
`f=(qB)/(2pim)`
`=(1.6xxx10^(-19)xx2)/(2 pi xx1.67xx10^(-27))`
` =(1.5xx2xx10^(-19+27))/(2pixx1.67)`
`f= (1.6xx2xx10^(8))/(2xx3.14xx1.67)`
`=(1.6xx10^(8))/(3.14xx1.67)`
`0.3051xx10^(8)`
`r=(mv)/(qB)`
`=(1.67xx10^(-27)xx3xx10^(7))/(1.6xx10^(-19)xx2)`
`=(5.01xx10^(-20))/(3.2xx10^(-19))`
`=(5.01xx10^(20+20))/(32)`
`(5.01)/(32)`
`=0.1565m`