With a labelled diagram, explain the construction and working of a cyclotron. Show that the frequency of the oscillator needed does not depend on the speed of the ions.

1. 1 · State the principle. An electric field in the gap speeds the charge up, and a magnetic field bends it into semicircles, again and again.
2. 2 · Draw the cyclotron. [Two dees D₁ and D₂ with a gap; ion source S at the centre; oscillator joined to the dees; dots for B; spiral path to an exit window; all labelled]
3. 3 · Describe the parts. Two hollow dees in a vacuum chamber, a strong uniform field B at right angles to them, and an oscillator across the dees.
4. 4 · Explain the working. The ion is accelerated across the gap, runs a semicircle inside a dee, and reaches the gap just as the voltage reverses. It gains energy at every crossing and spirals out to the exit.
5. 5 · Derive the frequency. qvB = mv²/R gives R = mv/qB; one round takes T = 2πR/v = 2πm/qB; so ν_c = qB/2πm, which has no v in it.
6. 6 · Link to life. Cyclotrons make radioactive medicines used in hospital scans.
7. 7 · Close in one line. So, one fixed oscillator frequency keeps the ions in step at every speed, until they reach the edge.

Scoring tip: Write the resonance condition in words too: the oscillator frequency equals the frequency of revolution of the ion.