1. The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 9

Question

1. The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. (a) Find the speed of the electron. (b) Find the speed of the proton. (c) By what factor does the speed of the electron exceed that of the proton? (d) Repeat the calculations in parts (a) through (c) assuming that both particles have kinetic energies of 2000 MeV. 2. When 1.00 g of hydrogen combines with 8.00 g of oxygen, 9.00 g of water is formed. During this chemical reaction, 2.86 x 105 J of energy is released. (a) Is the mass of the water larger or smaller than the mass of the reactants? (b) What is the difference in mass? (c) Explain whether the change in mass is likely to be detectible.

Explanation / Answer

reletevistic kinetic energy is
Ek = (y-1)mc^2

you know the rest energy
E = mc^2 = .511 and 938

electron:
2 = (y-1)*.511
y = 4.91
1/sqrt(1-v^2/c^2) = 4.91
.2035 = sqrt(1-v^2/c^2)
v^2/c^2 = .9586
v =0.979 c

do the same thing for the proton
2 = (y-1)*938
y = 1.002
1/sqrt(1-v^2/c^2) = 1.002
.9979 = sqrt(1-v^2/c^2)
v^2/c^2 = 0.00212
v = 0.0461 c

Note that for the proton since its kinetic energy was so small compared to its rest energy, we could have assumed it was non-relativistic and used the standard Ek = 1/2m*v^2 formula, though we would have had to find the protons mass

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