According to the theory of special relativity, as an object with mass approaches the speed of light, its relativistic mass increases. This effect is often referred to as "mass dilation" or "relativistic mass."
The concept of relativistic mass is derived from the equation:
m = m₀ / √(1 - (v²/c²))
where: m is the relativistic mass of the object, m₀ is the rest mass of the object (mass at rest), v is the velocity of the object, and c is the speed of light in a vacuum.
As the velocity (v) approaches the speed of light (c), the denominator of the equation approaches zero, causing the relativistic mass to increase towards infinity. However, it's important to note that this increase in mass is only apparent from the perspective of an observer in a different reference frame.
The concept of relativistic mass is now less commonly used in modern physics. Instead, physicists tend to focus on the object's rest mass, which remains constant regardless of its velocity. The increase in relativistic mass as velocity approaches the speed of light is better understood as an effect of energy, rather than a literal increase in mass.
In summary, as the velocity of an electron (or any object with mass) approaches the speed of light, its relativistic mass increases, but its rest mass remains the same.