Question

You wish to build a linear accelerator that will accelerate electrons to 85.9% of the speed of light. You want adjacent drift tubes to be at +5000V and -5000V potentials. To work this problem, you will need the relativistic formula for kinetic energy. (K = mv²/2 doesn't work for really fast particles.) Kinetic energy is K = E₀(γ – 1) where E₀ is the rest energy of an object. The rest energy of an electron is 0.511 MeV. [Remember that if we want to convert eV to SI units, all we have to do is put e = 1.60 × 10^–19 C into the equation; however, for this problem, it's easiest just to leave everything in eV.] How many drift tubes do you need?

The energy an electron gains is ΔK = qΔV in each gap. Just find the total kinetic energy by using the formula.
  Remember that you need one more drift tube than there are gaps.

Answer 1