The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938

Question

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 2.10 MeV. (a) Find the speed of the electron. _____________ c (b) Find the speed of the proton. ______________c (c) By how much does the speed of the electron exceed that of the proton? ______________c (d) Repeat the calculations assuming both particles have kinetic energies of 1900 MeV. electron's speed _____________m/s proton's speed ______________m/s exceeded speed ________________ m/s

Explanation / Answer

a) KE = ( -1) mc^2

=1/sqrt(1-v^2/c^2)

so

2.1 = ( 1/sqrt(1-v^2/c^2)-1) 0.511

v=0.98066 c

b) for proton

2.1 = ( 1/sqrt(1-v^2/c^2)-1) 938

v=0.0668 c

c) 0.98066-0.0668 =0.91386

d) now KE = 1900

1900 = ( 1/sqrt(1-v^2/c^2)-1) 0.511

v=0.9999999639 c

proton

1900 = ( 1/sqrt(1-v^2/c^2)-1) 938

v=0.9438 c

difference

0.9999999639-0.9438=0.0562 c

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