Introduction:
The thermal velocity of electrons in a conductor refers to the random motion of electrons due to their thermal energy. It is the average velocity at which electrons move within the conductor when heated. However, the average thermal velocity of electrons in a conductor is zero. This may seem counterintuitive, but it can be explained by understanding the principles of statistical mechanics and the behavior of electrons in a conductor.

Explanation:

1. Random Motion:
- Electrons in a conductor exhibit random motion due to their thermal energy. This means that they move in various directions with different velocities.
- The velocities of individual electrons can be positive or negative, depending on their direction of motion.
- The net velocity of the electrons is the sum of the velocities of all the individual electrons.

2. Cancellation of Velocities:
- While individual electrons may have different velocities, they cancel each other out when averaged over a large number of electrons.
- For every electron moving in one direction, there is another electron moving in the opposite direction with the same magnitude of velocity.
- As a result, the average velocity of the electrons becomes zero.

3. Randomness and Distribution:
- The random motion of electrons can be described by a statistical distribution.
- The distribution of velocities follows a Maxwell-Boltzmann distribution, which represents the probability of an electron having a particular velocity.
- The distribution is symmetric, with an equal probability of finding an electron with a positive or negative velocity.
- The average velocity is calculated by summing the velocities of all the electrons and dividing by the total number of electrons.

4. Conservation of Momentum:
- The cancellation of velocities and the resulting zero average velocity can also be explained by the principle of conservation of momentum.
- When two electrons collide, their momentum is transferred between them.
- The collisions between electrons lead to a redistribution of velocities, causing the cancellation of velocities and resulting in a zero average velocity.

Conclusion:
The average thermal velocity of electrons in a conductor is zero due to the random motion of electrons and the cancellation of velocities when averaged over a large number of electrons. This behavior can be explained by statistical mechanics and the principles of conservation of momentum.