Take an electron and a proton at any separation (for instance

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

Take an electron and a proton at any separation rr (for instance, inside a hydrogen atom). Use G=6.674×10−11 N m2 kg−2G = 6.674\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}, Coulomb's constant k=8.988×109 N m2 C−2k = 8.988\times10^9\,\mathrm{N\,m^2\,C^{-2}}, elementary charge e=1.602×10−19 Ce = 1.602\times10^{-19}\,\mathrm{C}, electron mass me=9.109×10−31 kgm_e = 9.109\times10^{-31}\,\mathrm{kg} and proton mass mp=1.673×10−27 kgm_p = 1.673\times10^{-27}\,\mathrm{kg}. ((a)) Write down the gravitational and electrostatic forces between the electron and the proton, and show that their ratio does not depend on rr. ((b)) Calculate this ratio. ((c)) For two protons 1 fm1\,\mathrm{fm} apart, the relative strengths strong : electromagnetic : weak : gravitational are 1:10−2:10−7:10−381 : 10^{-2} : 10^{-7} : 10^{-38}. Use this to compare gravity with the weak interaction at that separation. Then explain why the independence of rr found in (a) cannot carry this comparison out to the size of a hydrogen atom, 5.3×10−11 m5.3\times10^{-11}\,\mathrm{m}, where the ratio found in (b) still holds.

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