I read several times that the Planck scale is the energy scale at which the effects of gravity are comparable to the effects of the other fundamental forces.
How can I show that this actually happens at $10^{19}$ GeV?
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$\begingroup$ I found the answer myself: if one asks that the gravitational effect $G M^2/r$ is equal to the rest mass $M c^{2}$ one obtains $M c^{2}=10^{19}$ if the distance r is a natural unit of length. Regards $\endgroup$– FraCommented Mar 30, 2015 at 21:15
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I found the answer myself: requiring that the gravitational potential $GM^2/r$ is equal to the rest mass $Mc^2$, one obtains for r equal to a natural unit of length $Mc^2=1.22\times10^{19}$ GeV that is the Planck scale.