2. Calculate the thermal velocity of electrons in a conductor, taking that their kinetic energy equals the thermal energy kkBBTT with kB being the Boltzmann constant, at the following temperatures: a. 100 K b. 300 K c. 1000 K Compare the velocities you obtained in each answer to the speed of light.

(a). is 0.02% the speed of light.

(b)., is 0.04%  the speed of light.

(c). is 0.07% the speed of light.

Explanation:

The average kinetic energy is related to the thermal energy of the electrons in a conductor by the the relation

,

where is the mass of the electrons, is their average velocity, is the temperature of the conductor, and is the Boltzmann constant.

The equation, when solved for , gives

(a),

For , the thermal (average) velocity is

which when compared to the speed of light is

0.02% the speed of light.

(b).

Similarly, for  

which is

0.04% the speed of light.

(c).

Finally, for

which is

0.07% the speed of light.

We see that the average electron velocities we obtain are always less than 1% the speed of light, which means relativistic effects are negligible, for they are apparent at about 25% the speed of light.