Fermi energy

AIM: To determine the Fermi energy of the copper.
APPARATUS: DC Regulated power supply, Milliammeter, Voltmeter, Copper wire and Screw gauge.
PRINCIPLE: The energy of the highest occupied level by an electron at absolute zero temperature is called the Fermi energy. Fermi energy is given by,
EF = ½ mvF2
Where ‘m’ is the mass of the electron and ‘vF’ the Fermi velocity.
But vF = lF/t where lF is mean free path and t the relaxation time.
Since conductivity s = 1/r = L/RA = ne2t/m,
t = mL/ne2RA = mL/ne2Rpr2 [A=pr2 ]
\vF = ne2Rpr2 lF/ mL
Now EF = ½ mvF2 = ½ m (ne2Rpr2 lF/ mL)2
For Copper, n = 8.5 × 1028 /m3
lF = 53 × 10-9 m
e = 1.6 × 10-19 C
m = 9.1 × 10-31 Kg
\ EF = 7.16 × 10-2 × (r4/L2) × R2
But R = slope of the Voltage-Current graph.
\ EF = 7.16 × 10-2 × (r4/L2) × [Slope]2