An electron with an energy of 20 GeV (3.20 × 10^-⁹ J) moving in the +x direction collides head on with a stationary proton. After the collision, the electron travels in the -x direction. What is the momentum of the electron after the collision? Note that this is an ultrarelativistic collision so that the energy of the moving masses can be approximated by the expression E ≈ pc. The mass of a proton is 1.67 × 10^-²⁷ kg and that of an electron is 9.11 × 10^-³¹kg. A)2.5 × 10^-¹⁹ kg∙m/s B)5.0 × 10^-¹⁹ kg∙m/s C)1.1 × 10^-¹⁷ kg∙m/s D)2.2 × 10^-¹⁷ kg∙m/s E)2.7 × 10^-²² kg∙m/s

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Quizplus · Accepted Answer

The correct answer is A.The momentum of the electron after the collision is equal to the momentum of the electron before the collision but in the opposite direction. The momentum of the electron before the collision is:$$p = \frac{E}{c} = \frac{20 	ext{ GeV}}{3 	imes 10^8 	ext{ m/s}} = 6.67 	imes 10^{-19} 	ext{ kg m/s}$$Therefore, the momentum of the electron after the collision is:$$p = -6.67 	imes 10^{-19} 	ext{ kg m/s} = -2.5 	imes 10^{-19} 	ext{ kg m/s}$$

An Electron with an Energy of 20 GeV (3