EXPERIMENTAL ARRANGEMENT OF FERMI ENERGY
OBSERVATION:
Determination of radius of the copper wire (r):
Zero Error
=
Zero Correction
=
Least Count 
I
In mA
Value of 1 Pitch Scale Division
Total No. of Head Scale Divisions
=
mm
0
Voltage in volt
Tabulation to determine diameter of the copper wire (d):
Trial No.
PSR
In mm
HSR
ZE
ZC
TR= PSR+ ( HSR + ZC ) X LC
In mm
1.
2.
Radius of the given copper wire
Length of the Specimen wire
Tabulation to Determination of Fermi Energy
Trial No.
1.
2.
3.
4.
5.
6.
7.
Voltage
V
In volt
r = d/2 =………..mm
l= 2.0metre
Current
I
In mA
Fermi Energy
Aim:
Determination of Fermi Energy of the given copper wire.
Apparatus:
Copper wire, screw gauge, sample wire, ammeter, voltmeter, battery eliminator etc,.
Formula:
Fermi Energy
3.95x10 2 x Slope 2 xr 4
Ef 
eV
L2
Where
Ef
= Fermi energy in eV
V
slope    From graph
 I
R
= radius of the copper wire in mm
L
= length of the copper wire in m
Formula of Screw Gauge
TR
= PSR + (HSR+ZC)xLC
TR
= Total Reading in mm
PSR = Pitch Scale Reading in mm
HSR = Head Scale Reading
ZC
= Zero Correction
LC
= Least Count in mm
Theory:
The Fermi energy is the maximum energy occupied by an electron at 0K. By the Pauli Exclusion
Principle, we know that the electrons will fill all available energy levels, and the top of that
"Fermi Sea" of electrons is called the Fermi energy or Fermi level. The conduction electron
population for a metal is calculated by multiplying the density of conduction electron states g(E)
times the Fermi function f (E).
Procedure:
1. The circuit arrangement is made as shown in figure.
2. The voltage is varied gradually and the corresponding current values are noted down.
3. A graph can be plotted with the voltage along Y-axis and the current along the X-axis.
4. The slope of the graph gives the resistance of the given copper material.
5. The radius of the copper wire is measured using a screw gauge and the values are tabulated.
6. Length of the wire is measured by using a meter scale.
Determination of radius of the specimen wire using screw gauge
1. To find zero error, bring two metallic studs in contact and observe if the zero of the head
scale lies ‘n’ divisions above the horizontal (pitch) line then ZE= -n & ZC = +n, if the zero of
the head scale lies ‘n’ divisions below the pitch line then ZE =+n & ZC = -n, in case if the
zero of the head scale exactly coincides with pitch line then instrument has no zero error. i.e.,
ZE=0.
2. Keep the specimen between the metallic studs and bring it into gentle contact with the help of
head, note down the no. of division uncovered on pitch scale by the sleeve is the PSR, and
the division on the head scale is coinciding with the pitch line is the HSR, repeat the same
procedure for next trial, tabulate the readings & diameter of the wire is calculated and
average value of radius is obtained.
Result:
Fermi Energy of the given copper wire is given by =………….eV.