Gravity between two protons is about of their electrostatic repulsion

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Particle Physics & Quantum Fields · Particles, interactions and experiment

Particle Physics, Ch The particle zoo and the four interactions

Problem

Gravity between two protons is about 8.1×10−378.1\times10^{-37} of their electrostatic repulsion, at any separation where both 1/r1/r laws apply. Turn the comparison round. Use G=6.674×10−11 N m2 kg−2G = 6.674\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}, e2/(4πϵ0)=2.307×10−28 J me^2/(4\pi\epsilon_0) = 2.307\times10^{-28}\,\mathrm{J\,m}, mp=1.673×10−27 kgm_p = 1.673\times10^{-27}\,\mathrm{kg}, c=2.998×108 m s−1c = 2.998\times10^{8}\,\mathrm{m\,s^{-1}} and 1 MeV=1.602×10−13 J1\,\mathrm{MeV} = 1.602\times10^{-13}\,\mathrm{J}. ((a)) Two particles each carry charge ee and mass MM. Find the mass MM, in kilograms, for which their gravitational attraction exactly balances their electrostatic repulsion, and show that the answer does not depend on their separation. ((b)) Express MM in MeV/c2\mathrm{MeV}/c^2 and find the ratio M/mpM/m_p. ((c)) Show that (mp/M)2(m_p/M)^2 reproduces the ratio 8.1×10−378.1\times10^{-37}. The W+W^+ boson, of mass 80.37 GeV/c280.37\,\mathrm{GeV}/c^2, carries charge +e+e; by what factor does its mass fall short of MM?

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