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Physics (Second Semester) > Electrical Conductivity in Metals > Flashcards

Electrical Conductivity in Metals Flashcards

1
Q

According to Classical Free Electron Theory, what are free electrons ?

A

Freely moving valence electrons, confined to body

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2
Q

How does an applied electric field cause current in a metal, according to CFET ?

A

Current is a consequence of drift velocity of free electrons

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3
Q

What is the direction of the drift velocity of the free electrons(Conduction electrons) ?

A

Opposite to the applied electric field

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4
Q

What are free electrons equivalent to in CFET ?

A

Gas molecules

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5
Q

What are the expected to obey

A

Laws of Kinetic Theory of Gases

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6
Q

What is the energy associated with each electron in the absence of an electric field ?

A

(3/2)KT

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7
Q

What is K ?

A

Boltzmann Constant

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8
Q

What is the electric potential due to ionic cores ?

A

It is essentially constant throughout the metal

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9
Q

What is the magnitude of the force of attraction between the free electrons and the lattice ions ?

A

It is negligible

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10
Q

What about the repulsive force in between electrons ?

A

It is also negligible

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11
Q

What is mean free path, according to Kinetic Theory of Gases ?

A

It it the AVERAGE distance in between two successive collisions

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12
Q

Collisions of what ?

A

Collisions of two other molecules

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13
Q

How is it defined in CFET ?

A

It is the average distance travelled by the conduction electrons in between two successive collisions

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14
Q

Collisions with what ?

A

Lattice ions

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15
Q

What is mean collision time ?

A

It is the average TIME elapsed between two successive collisions

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16
Q

Collisions of what ?

A

An electron with lattice points

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17
Q

What is the probability of finding an electron moving in any given direction equal to ?

A

The probability of finding another electron in exactly the opposite direction in the ABSENCE of a field

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18
Q

What is current density ?

A

It is the current per unit area

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19
Q

Area of what ?

A

Cross section of an imaginary plane

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20
Q

What is the orientation of this imaginary plane ?

A

It is held normal to the direction of current

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21
Q

What is electric field ?

A

It is the potential drop per unit length of a conductor

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22
Q

What kind of conductors is this applicable to ?

A

Homogeneous conductors (Otherwise, integration is required)

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23
Q

What physical property does conductivity characterize ?

A

The conducting ability of a material

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24
Q

How is it quantified ?

A

It is the inverse of resistivity

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25
What is mobility of an electron ?
It is the drift velocity acquired by electrons in unit field
26
What was the contradiction of CFET in terms of molar specific heat of a gas at constant volume ?
It was found to be temperature dependent
27
How did CFET predict temperature dependence of electrical conductivity ?
Directly proportional to square root of temperature ?
28
How was it found to be experimentally ?
Inversely proportional to temperature
29
How did CFET say electrical conductivity depends on electron concentration ?
Electrical conductivity is directly proportional to electron concentration
30
What was the practical contradiction ?
The conductivites of Copper and Silver are much higher than Zinc and Cadmium
31
Which has the higher electron concentration ?
Zinc and Cadmium have higher electron concentration than Copper and Silver
32
What is an important assumption of Quantum Free Electron Theory (w.r.t. energy levels) ?
Energy levels are quantized
33
Energy levels of what ?
Conduction electrons
34
How are electrons distributed in allowed energy levels in QFET ?
According to Pauli's Exclusion Principle
35
What is a common postulate of both CFET and QFET (w.r.t. constant potential) ?
The free electrons travel in a constant potential, and stay confined to metal boundaries
36
What is another common postulate (w.r.t. negligible forces of attraction) ?
The electron-lattice attractive forces and electron-electron repulsive forces are both negligible
37
What is the nature of energy values of free electrons in electron gases, according to Classical - FET ?
They have continuous energy values
38
What is the nature of energy values of free electrons in electron gases, according to Quantum - FET ?
Energy levels are discrete ?
39
Why are energy levels discrete ?
Because the energy levels are discontinuous
40
How many electrons can have the same energy level in Classical - FET ?
Multiple electrons
41
How many electrons can have the same energy level in Quantum - FET ?
No two electrons can have the same energy level
42
Why ?
The free electrons obey Pauli's exclusion principle
43
What law explains the distribution of energy among free electrons in Classical - FET ?
Maxwell-Boltzmann statistics
44
What law explains the distribution of energy among the free electrons in Quantum - FET ?
Fermi- Dirac statistics
45
What does Fermi Dirac statistics impose a restriction on ?
It restricts the possible ways an electron can absorb energy from an external source
46
Why is the predicted specific heat capacity less for Quantum - FET ?
Only the electrons occupying energy levels close to Fermi Energy Level can absorb heat energy.
47
How many electrons does this include ?
A very small percentage. This reduces specific heat.
48
What was the flaw with Classical - FET ?
Maxwell Boltzmann statistics permitted ALL conduction electrons (irrespective of energy they already possess) to absorb heat energy
49
When is a body said to be free ?
When it is not under the influence of a force or a field
50
Does a free body have energy ?
A free body at rest does not have any energy
51
How is total energy calculated ?
It is the sum of kinetic energy (caused by motion) and potential energy(caused by position in field)
52
In macroscopic situations, are there restrictions on the energy value a body is allowed to have ?
Only at velocities comparable to the velocity of light.
53
Why ?
Relativity effects brings forth certain restrictions
54
What is the potential energy of an electron in an atom caused by ?
It depends on the distance from the protons
55
What is the kinetic energy of an electron in an atom cause by ?
Motion around the nucleus
56
What happens when an electron of an atom receives energy ?
It goes to another orbit
57
Can the energy levels of the orbits be anything ?
No, they are quantized
58
Why does quantization of the energy of an electron occur ?
Because it is in the influence of the field due to a proton
59
Does it apply to free electrons also ?
No, a free electron can have a continuous range of energy values
60
What are the energy levels of an isolated atom like ?
They are discrete
61
What happens when two atoms are bought close to each other ?
Each energy level gets split into two
62
What happens when N atoms are bought close to each other (like they are in a solid) ?
Each energy level is split into N energy levels
63
Does this mean that the energy values are now continuous ?
No, but they are practically continuous
64
What is an energy band ?
A bunch of quasi-continuous energy levels
65
What is a forbidden band or energy band gap ?
It is the energy band gap seperating two energy bands
66
What is valence band ?
The band above which all bands are empty and below which all are occupied
67
What is conduction band ?
The empty band above the valence band
68
What is density of energy level ?
It is the number of permitted energy levels per unit energy range
69
Why do we say density of energy STATES and not values ?
Each energy level is applicable to two energy states
70
What are the two energy state ?
1 for spin-up, 1 for spin-down
71
How is density of states g(E) defined ?
It is the number of energy states per unit energy range, centered at an energy E
72
Which band is density of states defined in ?
The valence band of the material
73
Why do we consider g(E) for a centered energy E ?
It is because there are a large number of permitted values. The density of energy level varies with energy in the band
74
Are there any other conditions for defining g(E) ?
It is calculated at constant volume.
75
What is Fermi level ?
The highest occupied level at zero degree absolute temperature
76
What is Fermi energy level ?
It is the energy corresponding to that
77
Why is it defined for zero degree absolute temperature ?
Because there is on external energy supply for the electrons at zero degree Kelvin.
78
What is Fermi factor ?
It is the probability of occupation of a given energy state for a material in thermal equilibrium
79
What is Fermi temperature ?
It is the T at which the average thermal energy of free electron in a solid is equal to Fermi Energy at 0 K.
80
What is Fermi velocity ?
The velocity of electrons which occupy Fermi level
81
Why do free electrons move in metals ?
Applied Electric field + Periodic potential due to lattice ions
82
What is effective mass of an electron ?
It is the mass the electron APPEARS to have
83
How is it different from the true mass ?
The true mass is the mass the electron would have if there was an external field alone.
84
What are the requirements of a perfect conductor ?
Infinite Conductivity | Infinite Collision Time
85
How can collision time be made infinity ?
Scattering of electrons should vanish
86
What are the main reasons for electron scattering ?
Lattice distortions | Lattice vibrations
87
Why do lattice vibrations persist even at zero degree absolute temperature ?
According to the uncertainty principle, certain vibrations persist. It is called zero point vibration.
88
Can perfect conductors be realised, even theoretically ?
No.
89
How are perfect conductors defined ?
Conductivity TENDS to infinity | Collision time TENDS to infinity
90
Are perfect conductors the same as super conductors ?
No

Physics (Second Semester) (6 decks)

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