What is the relativistic kinetic energy of an electron moving at a speed of 2.00 × 10⁸ m/s? (electron mass is 9.11 × 10−³¹ kg and c = 3.00 × 10⁸ m/s)

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Quizplus · Accepted Answer

The relativistic kinetic energy of an electron moving at a speed of 2.00 × 10⁸ m/s is given by:$$K = (\gamma - 1)mc^2$$where:* γ is the Lorentz factor, given by:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$* m is the mass of the electron, given by:$$m = 9.11 × 10^{-31} ext{ kg}$$* c is the speed of light, given by:$$c = 3.00 × 10^8 ext{ m/s}$$Substituting these values into the equation for the relativistic kinetic energy, we get:$$K = \left(\frac{1}{\sqrt{1 - (2.00 × 10^8 ext{ m/s})^2/(3.00 × 10^8 ext{ m/s})^2}} - 1 ight)(9.11 × 10^{-31} ext{ kg})(3.00 × 10^8 ext{ m/s})^2$$$$K = 2.80 × 10^{-14} ext{ J}$$Therefore, the correct answer is A.

What Is the Relativistic Kinetic Energy of an Electron Moving