Answers: Momentum electron (reltivistic): 12.50MeV/c, Momentum proton (reltivist

Question

Answers:

Momentum electron (reltivistic): 12.50MeV/c, Momentum proton (reltivistic): 150.5MeV/c

Momentum electron (classical): 3.502MeV/c, Momentum proton (classical): 150.1MeV/c

Kinetic Energy: 12MeV for both electron and proton

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An electron and a proton are each accelerated starting from rest through a potential difference of 12.0 million volts. Find the momentum (in MeV/c) and the kinetic energy (in MeV) of each, and compare with the results of using the classical formulas. (Give your answers to at least four significant figures.) Momentum Kinetic Energy (MeV) relativistioc classical electron 12 X12.5012 3.502 1.2 X12.00 proton 12150.5 1250. 1212.00 X150.1 1.2

Explanation / Answer

when accelerated through 12 MV

Kinetic energy = q deltaV = 12 MeV .......Ans(for both electron and prootn)

MOmentum:

Relativistic case: KE = (Y - 1 )m0 c^2

For electron:
  
12 = (Y - 1) (0.511 MeV/c^2) c^2

Y = 24.4

Y = 1 / sqrt[1 - (v/c)^2] = 24.42

v =0.9992 c

momentum =Y m v = (24.4)(0.511 MeV / c^2) (0.9992 c)

= 12.5 MeV/c

For proton:

mp = 938.28 MeV/c^2

12 = (Y - 1)(938.28)

Y = 1.013

1.013 = 1 / sqrt[1 - (v/c)^2]

v = 0.158c

momentum = (1.013)(928.28)(0.158c)

= 149 MeV/c

For classical:

Electron:

p = sqrt(2 m KE)

p = sqrt(2 x 0.511 x 12)

p = 3.502 MeV/c

Proton:

p = sqrt(2 x 928.38 x 12)

p = 149.3 MeV/c

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