According to the theory of relativity, specifically Albert Einstein's special theory of relativity, the mass of an object increases as its velocity approaches the speed of light. However, it's important to note that this increase in mass is relative and is not the same as an increase in rest mass.
In the context of an electron, it has a rest mass, which is the mass of the electron when it is at rest or moving at speeds much slower than the speed of light. The rest mass of an electron is a fundamental property and remains constant regardless of its motion.
As the velocity of an electron increases towards the speed of light, its relativistic mass comes into play. Relativistic mass is defined as the mass of an object when it is in motion, taking into account the effects of special relativity. The relativistic mass (m) of an electron is related to its rest mass (m₀) and its velocity (v) through the following equation:
m = m₀ / √(1 - v²/c²)
In this equation, c represents the speed of light in a vacuum.
As the velocity (v) of the electron approaches the speed of light (c), the denominator of the equation approaches zero, causing the relativistic mass (m) to increase. However, it's important to note that this increase in mass is only observed from an external reference frame. From the electron's frame of reference, its mass remains constant.
It's worth mentioning that the concept of relativistic mass is not commonly used in modern physics. Instead, physicists prefer to work with the concept of relativistic energy, which takes into account both the rest energy (mc²) and the kinetic energy of the moving particle. The total energy of a particle, including its rest energy, increases as its velocity approaches the speed of light.