Question

The Fermi energy in copper is 7.04 eV. Compare the approximate average

energy of the free electrons in copper at room temperature (kT = 0.025 eV) with their

average energy if they followed Maxwell-Boltzmann statistics​

Answer 1

Given that,

Fermi energy = 7.04 eV

Energy kT=0.025 eV

We need to calculate the average energy

Using formula of fermi energy

$E=\dfrac{3}{5}E_{f}$

Where, $E_{f}$ = fermi energy

Put the value into the formula

$E=\dfrac{3}{5}\times7.04$

$E=4.22\ eV$

For room temperature,

We need to calculate the average kinetic energy

Using formula of energy

$E=\dfrac{3}{2}kT$

Where, k = boltzmann constant

T = temperature

Put the value into the formula

$E=\dfrac{3}{2}\times0.025$

$E=37.5\ m\ eV$

Hence, Their average energy are 4.22 eV and 37.5 meV