A cyclotron has an oscillatory frequency of `10MHz` and a dee radius of `60cm`. Calculate the magnetic field required to accelerate the deutrons of mass `3*3xx10^(-27)kg` and charge `1*6xx10^(-19)C`. Find the energy of deutrons emerging from the cyclotron.

Answer

`1*3T`; `14*74MeV`

Explanation

Here, `v=10xx10^6Hz=10^7Hz`, `r=0*60m`
`m=3*3xx10^(-27)kg`, `q=1*6xx10^(-19)C`
As `v=(qB)/(2pim)`, so, `B=(2pimv)/(q)`
`:. B=(2xx3*142xx(3*3xx10^(-27))xx10^7)/((1*6xx10^(-19)))=1*3T`
Max. KE of the emerging deutron is
`K_(max)=(q^2B^2r^2)/(2m)`
`=((1*6xx10^(-19))xx(1*3)^2xx(0*6)^2)/(2xx(3*3xx10^(-27)))J`
`=((1*6xx10^(-19))^2xx(1*3)^2xx(0*6)^2)/(2xx(3*3xx10^(-27))xx(1*6xx10^(-13)))=MeV`
`=14*74MeV`