Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h− (the hydride ion, which has one proton and two electrons) to an energy of 5mev to 20mev. this ion has a mass very close to that of a proton because the electron mass is negligible−about 1/2000 of the protons mass. a typical magnetic field in such cyclotrons is 1.7 t .part awhat is the speed of a 5.0-mev h−? express your answer with the appropriate units. part bif the h− has energy 5.0mev and b= 1.7 t , what is the radius of this ions circular orbit? express your answer with the appropriate units.

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?