In the January 1983 issue of the American Journal of Physics, Edward Purcell published a one-page "Round-Number Handbook of Physics" (see e.g. http://lemeshko.blogspot.com/2008/06/one-page-round-number-handbook-of.html). In the section on unit conversions, one line reads: "pc(eV) = 300 Br(G cm)". Does anyone have any idea what this means? I note that 1 eV/(G cm) seems to be closely related to the elementary charge, but I still can't quite figure out what this line is about.
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It's the cyclotron radius $r$ for a particle with momentum $p$ in a magnetic field $B$,
$$ |q|Br = p_\perp, $$
for the common case where the particle has one quantum of charge.
The numerical conversion constant 300 has the same first significant figure as the speed of light, $c = \rm 3\times10^8\,m/s$. The "rule of thumb" multiplies both sides by $c$ so that both have energy units --- the electron-volt is a convenient unit of energy for subatomic particles. The numerical factor ends up as $3\times 10^2$ because of the difference between gauss-centimeters and the SI unit, tesla-meters.
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$\begingroup$ Yes, this looks right, thanks so much. Specifically, it appears to be the cyclotron radius for a particle of charge $e$. $\endgroup$ Commented Jul 1, 2018 at 1:08
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