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I would like to know if the following relation, which numerically holds true according to the data available on wikipedia, can be analytically deduced from the current standard physic and model of a proton:

R = 4 x L x ( M / m )

=4 x 1.61619997e−35 x 2.1765113e−8 / 1.67262177774e−27 = 8.412368e-16 m which is correct according to wikipedia.

With R = charge radius of a proton, L = planck length, M = Planck mass, m = Proton mass

As this relation is very simple and as it only uses fundamental constants such as planck length and planck mass, I would expect this relation to be found easily, maybe "by definition" or trivial equality. But I can't find this equality on the web in any standard physic document.

Can you tell me how to prove this? Is it a trivial equality?

(Please note I am not a physicist, but I have a scientific background)

Thank you very much!

Cyril

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# Charge radius of a proton as a function of its mass

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