Final answer:
The momentum of an electron traveling at 0.980c is calculated using the principles of relativistic physics and includes the Lorentz factor. The correct formula for its momentum is mₑ × (1 - 0.980^2)^{0.5}, where mₑ represents the rest mass of the electron.
Step-by-step explanation:
Calculating the Momentum of an Electron
When calculating the momentum of an electron moving at relativistic speeds (speeds approaching the speed of light), we cannot use the classical mechanics formula p = mv straightforwardly. Instead, we have to consider the principles of relativistic physics, specifically those taught by Einstein's Special Theory of Relativity. At speeds close to the speed of light (c), we need to account for the increase in mass that results from relativistic effects.
According to the theory of relativity, the momentum (p) of an object is given by the equation p = γmv, where m is the rest mass of the object, v is its velocity, and γ (gamma) is the Lorentz factor, which can be calculated using γ = (1 - (v/c)^2)^{-0.5}. Therefore, the correct expression for the momentum of an electron traveling at 0.980c would be the application of the Lorentz factor, leading to answer choice d: mₑ × (1 - 0.980^2)^{0.5}, where mₑ is the rest mass of the electron.
This equation shows that as the velocity of the electron approaches the speed of light, the Lorentz factor increases, indicating a significant increase in momentum due to relativistic effects. Thus, the correct calculation of the momentum of an electron at 0.980c is not simply its mass times the velocity but must include the relativistic adjustments provided by the Lorentz factor.