You wish to build a linear accelerator that will accelerateelectrons to ?=89 % of the speed of light. You want adjacent drifttubes to be at +5000V and −5000V potentials. To work this problem,you will need the relativistic formula for kinetic energy. (?=??2/2doesn't work for really fast particles.) Kinetic energy is?=?0(?−1) where ?0 is the rest energy of an object. The rest energyof an electron is 0.511 MeV. [Remember that if we want to converteV to SI units, all we have to do is put ?=1.60×10−19 C into theequation; however, for this problem, it's easiest just to leaveeverything in eV.] How many drift tubes do you need? Hints: Theenergy an electron gains is ??=??? in each gap. Just find the totalkinetic energy by using the formula. Remember that you need onemore drift tube than there are gaps. Range of answers: 45 to115
hint: β= 90.7 %, correct answer is 72
β= 86.9, correct answer is 54
