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

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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Chiecrere2f
Relativity should start to show up at kinetic energies approaching a particle's rest mass. So, we have:
$\begin{array}{rl}qV& =m{c}^{2}\\ V& =\frac{m{c}^{2}}{q}\end{array}$
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
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.