The mass of the proton is \(m_{p}=1.6710^{-27} \mathrm{~kg}\), that of the electron 1840 less than \(m_{p}\). The Coulomb potential energy for the electromagnetic interaction between electron and proton in the hydrogen atom (fundamental state) is of the order of \(10 \mathrm{eV}\), where \(1 \mathrm{eV}=1.610^{-19}\) J. Estimate the ratio \(R\) between gravitational potential energy and electromagnetic potential energy.