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WorksheetsUnit 1
Total questions: 25
Worksheet time: 13mins
Fermi Distribution Function
Distribution of electrons among same energy level
Distribution of electrons among various energy level
Distribution of electrons in between the energy level
Distribution of electrons in and out of the energy level
Fermi Dirac Statistics
Probability function of an electron occupancy for energy level at absolute temperature
Probability function of an electron occupancy for energy level at same temperature
Probability function of an electron occupancy for energy level at different temperature
Probability function of an electron occupancy for energy level at various temperature
Equation of fermi dirac statistics
1/1 + e(E - EF)/kT)
1/1 + e(E + EF)/kT)
1/1 - e(E - EF)/kT)
1/1 + e(E + EF)/kT)
Degenerate states
Different energy eigen value and different eigen functions
Different energy eigen value and same eigen functions
Same energy eigen value but different eigen functions
different energy eigen value same eigen functions
Energy of the particle
E = nh2 / 8ma2
E = h2 / 8ma
E = nh3 / 8ma2
E = nh2 / 8ma3
If the theory used quantum concepts then it is known as
Classical free electron theory
Quantum free electron theory
Zone free electron theory
Band free electron theory
Postulates of quantum free electron theory
Electrons have wave nature
Allowed energy levels of an electron are quantized
free electrons obey fermi - Dirac statistics
Potential energy of an electron is uniform or constant within the metal
Failures of Classical free electron theory
All electrons absorb the supplied energy
semiconductors and insulators cannot be explained by this theory
Photoelectric and compton effect and black body radiation can be explained
Paramagnetic material is inversely proportional to temperature.
success of classical free electron theory
Used to verify Ohms law
Used to explain electrical and thermal conductivity
Used to derive wiedmann franz law
Explain the optical properties of metals
Lorentz number
Ratio of thermal conductivity to the product of electrical conductivity and absolute temperature of the metal is constant
Ratio of thermal conductivity to the product of electrical conductivity and various temperature of the metal is constant
Ratio of thermal conductivity to the product of electrical conductivity and absolute temperature of the metal is not constant
Ratio of thermal conductivity to the product of electrical conductivity and various temperature of the metal is not constant
Wiedmann franz law
K/σ = T
K = T/σ
K/σ = T/σ
K/σ = T2
Expression for electrical conductivity of a metal
σ = q / t A 2E
σ = q / t A
σ = t / qA E
σ = q / t A E
Drift velocity
Average velocity acquired by the free electrons of a metal in a smae direction by the application of an electrical field
Average velocity acquired by the free electrons of a metal in a opposite direction by the application of an electrical field
Average velocity acquired by the free electrons of a metal in a particular direction by the application of an electrical field
Average velocity acquired by the free electrons of a metal in a both direction by the application of an electrical field
Mean free path
The average distance travelled by a free elecron between either of two successive collisions
The average distance travelled by a free elecron between any two successive collisions
The average distance travelled by a free elecron between any three successive collisions
The average distance travelled by a free elecron between the successive collisions
Probability of occupation for E < EF at T = 0K then F(E) is equal to
1
0
-1
2
Density of energy states Z (E) dE
N(E) + dE
N(E)=dE
N(E) - dE
N(E)/dE
Carrier concentration in metals nc
= Z (E) - F (E) dE
= Z (E) + F (E) dE
= Z (E) F (E) dE
= Z (E) * F (E) dE
energy band in a crystalline solid
The free electrons move in a periodic potential produced by negative ion cores
The free electrons move in a periodic potential produced by positive ion cores
The free electrons move in a periodic potential produced by both positive and negative ion cores
The free electrons move in a periodic potential produced by either positive or negative ion cores
The band formed from atomic energy levels containing valence electrons
covalent band
valence band
forbidden band
both a and b
In germanium the forbidden gap is of the order of 0.7eV while in case of silicon, it is the order of
1.3 eV
1.2 eV
1.1 eV
1.0 eV
in semiconductor the conductivities are of the order of
103 Ωm
101 Ωm
104 Ωm
102 Ωm
Effective mass of an electron is denoted is
m*
n*
r*
t*
The effective mass of an electron is positive, d2E/dk2 also
negative
positive
both a and b
neutral
Drawback of Classical free electron theory related to Lorentz number
Theoritical value 1.34 experimental value is 2.34
Theoritical value 1.12 experimental value is 2.24
Theoritical value 1.02 experimental value is 2.02
Theoritical value 1.22 experimental value is 2.22
Tight binding" model suggests that this quantum mechanical model describes the
freely bound electrons in solids
Compactly bound electrons in solids
tightly bound electrons in solids
loosely bound electrons in solids
