Suppose a cyclotron is operated at an oscillator frequency of 12 MHz (Mega-Hertz) and has a radius of R=53 cm. A deuteron is the nucleus of deuterium, an isotope of hydrogen, consisting of a proton and a neutron, and therefore having the same charge as a proton is to be accelerated in the cyclotron. Its mass, m=3.24 x10-27 kg. Find: (a) What is the magnitude of the magnetic field needed to accelerate the deuteron in the cyclotron? (b) The relationship of the radius of the path, R and the velocity of the deuteron is given by: R= mv/qB, what is the speed of the deuteron in the circular path? (c) What is the resulting kinetic energy of the deuteron?

Suppose a cyclotron is operated at an oscillator frequency of 12 MHz (Mega-Hertz) and has a radius of R=53 cm. A deuteron is the nucleus of deuterium, an isotope of hydrogen, consisting of a proton and a neutron, and therefore having the same charge as a proton is to be accelerated in the cyclotron. Its mass, m=3.24 x10-27 kg. Find: (a) What is the magnitude of the magnetic field needed to accelerate the deuteron in the cyclotron? (b) The relationship of the radius of the path, R and the velocity of the deuteron is given by: R= mv/qB, what is the speed of the deuteron in the circular path? (c) What is the resulting kinetic energy of the deuteron?