How do we calculate the relativistic energy equivalent contained in one proton in #"MeV"#?

1 Answer
Truong-Son N.
Feb 23, 2017

Consider that an electron acts as a wave. It has a spin of #pm1/2#. Similarly, a proton has a spin of #pm1/2#. Either particle can be treated using

#E = mc^2#,

since both have significant wave characteristics (though they are less prominent in protons).

The rest mass of a proton is #1.672621898 xx 10^(-27)# #"kg"#. Calculating its energy is a simple conversion:

#E = (1.672621898 xx 10^(-27) "kg")(2.99792458xx10^8 "m/s")^2#

#= 1.50327759 xx 10^(-10) "J"#

Now that we're in units of energy, we can convert from #"J"# to #"eV"#.

#1.50327759 xx 10^(-10) cancel"J" xx cancel"1 eV"/(1.602176565 xx 10^(-19) cancel"J") xx ("1 MeV")/(10^6 cancel"eV")#

#=# #color(blue)("938.272 MeV")#

This website gives #938.28# #"MeV"#. Pretty close.

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