A magnetic fi eld of 1.4 T is used to accelerate 10.0- MeV protons in a cyclotron. (a) What is the radius of the magnet? (b) What is the cyclotron frequency?

In nuclear power plants, atoms are split apart to form smaller atoms releasing energy 20 in a process called nuclear fission. Calculate the electrical power that is released in one hour due to splitting 200 g of Uranium-235, taking the disintegration energy per event to be 208 MeV.

6.13 Alpha particles are accelerated in a superconducting cyclotron operating with a magnetic field of 4 T. If the energy of extracted a particles is 12.5 MeV, calculate the value of the extraction radius in cm. 6.14 Calculate the cyclotron frequency in Problem 6.13.

Beams of p- mesons are used in radiation therapy for certain cancers. The energy comes from the complete decay of the p- to stable particles. (a) Write out the complete decay of a p- meson to stable particles. What are these particles? (b) How much energy is released from the complete decay of a single p- meson to stable particles? (You can ignore the very small masses of the neutrinos.) (c) How many p- mesons need to decay to give a dose of 50.0 Gy to 10.0 g of tissue? (d) What would be the equivalent dose in part (c) in Sv and in rem? Consult Table 43.3 and use the largest appropriate RBE for the particles involved in this decay.

For synchronous particles to remain on a constant radius in a synchrotron, show that the time derivative of the magnetic field is given by dB BATtum dt 2xqpR where ATturn is the kinetic energy gain per turn, R is the radius and p the bending radius, q the charge of a particle, ẞ=v/c. Assume the particles are accelerated on crest in a synchrotron of 10 GeV (kinetic energy) where the magnetic field reaches 1.5 Tesla in one second, following a linear variation. Calculate the bending radius and assuming R~1.5p, evaluate the accelerating voltage in kV.

To measure the muon magnetic moment a 2.9-T uniform magnetic field is used. How much energy is stored in the field if the experimental chamber where the field is created has dimensions of 65 cm×35 cm×60 cm?   The energy, ? How long will it take to “switch on” the field if the experiment uses a 1.5-kW power supply? Time ?

Please answer questions d and e only. Thanks!