# Problem: A proton (with a rest mass m=1.67×10−27 kg) has a total energy that is 4.00 times its rest energy.a. What is the kinetic energy Ek of the proton? Express your answer in billions of electron volts to three significant figures.b. What is the magnitude of the momentum p of the proton? Express your answer in kilogram-meters per second to three significant figures.c. What is the speed v of the proton? Express your answer as a fraction of the speed of light to four significant figures.

###### FREE Expert Solution

Total energy:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{m}}{{\mathbf{c}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{K}}{\mathbf{.}}{\mathbf{E}}}$

Kinetic energy, K.E:

K.E = E - mc2

But, E = 4.00 (mc2)

K.E = 4.00 (mc2) - mc2 = 3.00 mc2

m = m=1.67×10−27kg, c = 3.0 ×108 m/s

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###### Problem Details

A proton (with a rest mass m=1.67×10−27 kg) has a total energy that is 4.00 times its rest energy.

a. What is the kinetic energy Ek of the proton? Express your answer in billions of electron volts to three significant figures.

b. What is the magnitude of the momentum p of the proton? Express your answer in kilogram-meters per second to three significant figures.

c. What is the speed v of the proton? Express your answer as a fraction of the speed of light to four significant figures.