Medical cyclotrons need efficient sources of protons to inject into their center. in one kind of ion source, hydrogen atoms (i. e., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionize it. one such source uses a magnetic field of 90 mt, and the electrons' kinetic energy is 1.6 ev. part aif the electrons travel in a plane perpendicular to the field, what is the radius of their orbits?

The frequency of a tuning fork can be found by the method shown. a long tube open at both ends is submerged in a beaker of water, and the vibrating tuning fork is placed near the top of the tube. the length l of the air column is adjusted by moving the tube vertically. the sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. the smallest value for l for which a peak occurs in sound intensity is 7 cm. l what is the frequency of the tuning fork? the speed of sound in air is 345 m/s. answer in units of hz