What is thermal speedof free electrons in a conductor? Estimate the order of thermal speed at 27 c

Dear Student,

Solution:

The thermal velocity of electrons is usually taken as their rms velocity while treating the electrons as an ideal gas. Their rms velocity is given by:

v_rms =$\sqrt{\frac{3k_{B}T}{m}}$
where k_B is Boltzmann’s constant, T is the absolute temperature, and m is the mass of the electron.

k_B= 1.38× 10^-23 m² kg s^-2 K^-1
m_e= 9.1× 10^-31 kg
For T=27+273= 300 K,

substituting the values, v_{rms= 116826 m/s= 116.8 km/s}

Thermal just means that the electrons are in thermal equilibrium with their surrounds. It is a means of indicating the energy of the electrons.

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