An electron (rest mass ) has kinetic energy

PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

Particle Physics, Ch Scales, units and the four-momentum

Problem

An electron (rest mass mec2=0.511 MeVm_ec^2 = 0.511\,\mathrm{MeV}) has kinetic energy T=1.000 MeVT = 1.000\,\mathrm{MeV}. Someone works out its momentum as follows: "The total energy is E=T+mec2=1.511 MeVE = T + m_ec^2 = 1.511\,\mathrm{MeV}, so γ=E/(mec2)=2.957\gamma = E/(m_ec^2) = 2.957. This means the electron's relativistic mass has grown to mrel=γmem_{rel}=\gamma m_e, giving mrelc2=1.511 MeVm_{rel}c^2 = 1.511\,\mathrm{MeV}. Since γ\gamma is large, the electron is moving very nearly at the speed of light, so take v≈cv \approx c. Then p=mrelv≈mrelcp = m_{rel}v \approx m_{rel}c, giving p=1.511 MeV/cp = 1.511\,\mathrm{MeV}/c." (a) Find the electron's correct momentum using the energy-momentum relation, keeping rest mass as the only mass that appears. (b) Say which steps of the quoted working are exact and which step is an approximation, explain why this book keeps the word mass for rest mass alone, and state by what percentage the final momentum is too large.

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