Question

The 3.20-km-long SLAC produces a beam of 50.0-GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?

$3.33 \textrm{ MV}$

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Video Transcript

This is College Physics Answers with Shaun Dychko. Electrons in the Stanford Linear Accelerator are accelerated to an energy of 50 gigaelectron volts—that's the kinetic energy. They have a charge of, you know, 1.602 times 10 to the minus 19 coulombs since that's the elementary charge and they are accelerated through fifteen thousand different accelerator tubes. Now the amount of potential energy that they gain by going through a single tube is equal to the potential energy difference of that single tube which will be the charge multiplied by the joules per coulomb or voltage of the tube. And the total energy of all of these tubes together will be the number of tubes multiplied by the potential energy of each one and that will be the kinetic energy in total of the electrons—50 gigaelectron volts. So we substitute

*Q ΔV*in place of*ΔPE*here and then we solve for the voltage*ΔV*; that's the voltage of a single accelerator tube and we divide both sides by*NQ*. So we have the total kinetic energy of the electrons converted into joules and then divide by the number of accelerating tubes times the elementary charge*Q*. And that gives 3.33 megavolts is the voltage of each accelerating tube.