In a cyclotron the frequency of alternating current is 12 MHz and the radii of its dee is `0.53m`. What is the kinetic energy of the proton beam produced by the cyclotron ? Given mass of proton `=1.67xx10^(-27)` kg and charge `=+1.6xx10^(-19)C`.

Explanation

Kinetic energy of proton,
`E=(q^(2)B^(2)R^(2))/(2m)=((1.6xx10^(-19))^(2)xx(0.53)^(2))/(2xx(1.67xx10^(-27)))`
`=1.34xx10^(-12)J=(1.34xx10^(-12))/(1.6xx10^(-19))eV`
`=8.375xx10^(6)eV=8.375MeV`.