A cyclotron's oscillator frequency is `10MHz`. What should be the operating magnetic field for accelerating `alpha`-particles ? If the radius of the dees is `60cm`, what is the kinetic energy of the `alpha`-particle beam produced by the accelerator? Given, charge of an electron is `1*6xx10^(-19)C`, mass of each nucleon is `1*67xx10^(-27)kg`.

Answer

`1*312T`; `29*68MeV`

Explanation

`v=(Bq)/(2pim)` or `B=(2pimv)/(q)`
Here, `m=4xx(1*67xx10^(-27))kg`,
`q=2e=2xx1*6xx10^(-19)C`
`v=10MHz=10xx10^6Hz=10^7Hz`.
`E_(max.)=(B^2q^2R^2)/(2m)=((4pi^2m^2v^2)/(q^2))xx(q^2R^2)/(m)`