For an electron in motion with a speed less than the speed of light but greater than zero, we can relate its momentum and energy using the relativistic equations.
The relativistic energy-momentum relation for a particle with mass is given by:
E² = (pc)² + (mc²)²
Where E is the total energy of the particle, p is its momentum, c is the speed of light, and m is its rest mass.
For an electron, which has a nonzero rest mass, we can rearrange this equation to solve for the momentum:
p = √(E² - (mc²)²) / c
Similarly, we can solve for the energy:
E = √((mc²)² + (pc)²)
These equations show that the energy and momentum of an electron are interrelated. As the momentum increases, so does the energy. The rest mass term (mc²) accounts for the energy of the electron at rest, while the term (pc) represents the kinetic energy associated with its motion.
It is important to note that as the speed of the electron approaches the speed of light, these equations become more significant, and the classical approximation for momentum (p = mv) is no longer valid. At high speeds, relativistic effects must be taken into account.