What is the minimal voltage between anode and cathode in a linear accelerators to achieve speeds where relativity starts to show?

Makaila Simon 2022-09-27 Answered
What is the minimal voltage between anode and cathode in a linear accelerators to achieve speeds where relativity starts to show?
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Answers (2)

Chiecrere2f
Answered 2022-09-28 Author has 9 answers
Relativity should start to show up at kinetic energies approaching a particle's rest mass. So, we have:
q V = m c 2 V = m c 2 q
Using the values for the electron, we get about 5 × 10 5 V for electrons to turn relativistic. Protons are going to take longer, an anything heavier will take yet longer, since m typically grows a lot faster than q. If we want to get more precise than this, we are going to need to start talking precisions and things.
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Orion Cervantes
Answered 2022-09-29 Author has 2 answers
Define the limits of "starts to show" that you care about.
Electrons are significantly relativistic at 100 kV and measurably so at a few 10s of kV.
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