Derive the range relation for heavy charged particles (mass m. charge ze) with the same speed as a proton with mass mp and range rp. the medium is the same for both particles. start from the simplified energy and z dependence of the stopping power.

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