1. Background In a cyclotron, protons are kept moving in a circular path by a uniform magnetic field at right angles to the plane of the path. Only a few centimetres in diameter, the Lawrence cyclotron accelerated protons to energies of 80 keV.

2. 1.What is the velocity of a proton with an energy of 80 keV? mass of proton = 1.7 x 10 –27 kg charge on proton = 1.67 x 10 –19 C using Remembering that 1 eV =1.6 x 10 -1 9 J 80keV = (80 x 10 3 x 1.6 x10 -19 ) so v =3.9 x10 6 ms -1

3. 2.. The largest possible path had a radius of about 50 mm. What strength of magnetic field must have been used? r =50mm The centripetal force (mv 2 /r) is provided by the force on the proton due to the magnetic field (BqV) r = 50mm ( the path radius )

5. 3.What would be the radius of the path followed by a proton with half this maximum energy in the same field? Because we know the energy we can calculate the new velocity of the proton. Its energy is half the original so its velocity is.

6. How long would it take 80 keV protons to travel once round their path? How long would it take for those with half this energy? Circular motion theory gives us from 3 and T is the same for all velocities and hence all particle energies

7. Constructed of two D -shaped chambers (later called ‘dees’ because of their shape), the cyclotron worked by giving particles of any energy, on their respective paths, a push every time they had completed half an orbit. 5.How was it possible for particles of differing energy all to be accelerated together? We have just seen that the time taken for an orbit is independent of its energy so particles of different energies will orbit at the same speed e the same mass and chargeprovided that they hav