i just state the formula and the usage of it.

the basic equation is

E^2 = (p c)^2 + (m c^2)^2

where E is total energy, p is momentum

here we can see the advantage of using MeV as unit of mass. the equation is now further simplified by using MeV/c as momentum unit.

E^2 = p^2 + m^2

which is Pythagorean theorem!

the speed of the particle is from the formula

\beta = \frac {v}{c} = \frac {p}{E}

For example, proton mass is 940 MeV/c2, if we say an proton is moving at 94MeV, or a 94 MeV proton. we mean, the KINETIC Energy (K.E.) of proton is 94MeV. The total energy is

E = m + K.E.

Thus, a 94 MeV proton is moving at 41.7% of light speed. by using a right-angle triangle of base 10, side 11, and the hight is Square-Root 21.

another way around is, a proton at 90% speed of light, how much K.E. it has? which is around 3000 MeV or 3 GeV [Giga eV]

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