Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency `(rf)` field were doubled.

Explanation

Time period of revolution of charged particle in cyclotron, `T=(2pim)/(Bq)`
Frequency of revolution, `v=1/T=(Bq)/(2pim)`
If `v^'=2v`, then `T^'=1/v^'=(1)/(2v)=1/2xx(2pim)/(Bq)=(pim)/(Bq)=(pim)/(Bq)=a const ant`.
It means, the charged particle will accelerate and decelerate alternately between the dees of cyclotron. So the radius of path in the dees will remain unchanged.