What is the relativistic momentum of a proton with an energy of 1020 eV? To ente

Question

What is the relativistic momentum of a proton with an energy of 1020 eV? To enter the kinetic energy, set the units to GeV, which is billions of eV (109). Then multiply by 1 followed by the right number of zeros to bring it to 20. Answer to three parts accuracy. Use scientific notation in the format The units are kg m/s. Do not include these units in your answer. Now calculate the (classical) momentum of the baseball. Since the relativistic equations always hold, but become the equivalent of classical at low speeds, we can use the same tool for this answer as well. Change "relativistic momentum proton" to just "relativistic momentum". Click on "use velocity instead", and enter the velocity and mass in compatible units. Use 60 mph for the velocity and 5 oz for the "mass" (although that's not strictly correct, as we have learned!), taking the values from the activity page. (Do NOT use the approximate conversions used in the Activity as these are not accurate enough.) The final answer should be in kg m/s, same as the previous answer. Do not include the units in your answer. Now change the header to "relativistic momentum electron", and click on "use kinetic energy instead". Enter 1020 eV as you did for the proton, and find the momentum in kg m/s. Use scientific notation in the same format as for the first question.

Explanation / Answer

1)

E = K - m c^2 = 1e20 - 938.3e6 = 99999999999061700000 eV

E = gamma m c^2

==> gamma = 99999999999061700000/938.3e6 = 106575722050

gamma = 1/(1-(v/c)^2)^0.5

106575722050 = 1/(1-(v/c)^2)^0.5

==> v = 0.9999999999999999999999559796555 c

p = gamma m v

p = 106575722050 * 1.673e-27*0.9999999999999999999999559796555*3e8

p = 5.35E-8 kg.m/s

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