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

Electrical Conductivity in Metals Flashcards

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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
Q

What is mobility of an electron ?

A

It is the drift velocity acquired by electrons in unit field

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26
Q

What was the contradiction of CFET in terms of molar specific heat of a gas at constant volume ?

A

It was found to be temperature dependent

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27
Q

How did CFET predict temperature dependence of electrical conductivity ?

A

Directly proportional to square root of temperature ?

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28
Q

How was it found to be experimentally ?

A

Inversely proportional to temperature

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29
Q

How did CFET say electrical conductivity depends on electron concentration ?

A

Electrical conductivity is directly proportional to electron concentration

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30
Q

What was the practical contradiction ?

A

The conductivites of Copper and Silver are much higher than Zinc and Cadmium

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31
Q

Which has the higher electron concentration ?

A

Zinc and Cadmium have higher electron concentration than Copper and Silver

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32
Q

What is an important assumption of Quantum Free Electron Theory (w.r.t. energy levels) ?

A

Energy levels are quantized

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33
Q

Energy levels of what ?

A

Conduction electrons

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34
Q

How are electrons distributed in allowed energy levels in QFET ?

A

According to Pauli’s Exclusion Principle

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35
Q

What is a common postulate of both CFET and QFET (w.r.t. constant potential) ?

A

The free electrons travel in a constant potential, and stay confined to metal boundaries

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36
Q

What is another common postulate (w.r.t. negligible forces of attraction) ?

A

The electron-lattice attractive forces and electron-electron repulsive forces are both negligible

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37
Q

What is the nature of energy values of free electrons in electron gases, according to Classical - FET ?

A

They have continuous energy values

38
Q

What is the nature of energy values of free electrons in electron gases, according to Quantum - FET ?

A

Energy levels are discrete ?

39
Q

Why are energy levels discrete ?

A

Because the energy levels are discontinuous

40
Q

How many electrons can have the same energy level in Classical - FET ?

A

Multiple electrons

41
Q

How many electrons can have the same energy level in Quantum - FET ?

A

No two electrons can have the same energy level

42
Q

Why ?

A

The free electrons obey Pauli’s exclusion principle

43
Q

What law explains the distribution of energy among free electrons in Classical - FET ?

A

Maxwell-Boltzmann statistics

44
Q

What law explains the distribution of energy among the free electrons in Quantum - FET ?

A

Fermi- Dirac statistics

45
Q

What does Fermi Dirac statistics impose a restriction on ?

A

It restricts the possible ways an electron can absorb energy from an external source

46
Q

Why is the predicted specific heat capacity less for Quantum - FET ?

A

Only the electrons occupying energy levels close to Fermi Energy Level can absorb heat energy.

47
Q

How many electrons does this include ?

A

A very small percentage. This reduces specific heat.

48
Q

What was the flaw with Classical - FET ?

A

Maxwell Boltzmann statistics permitted ALL conduction electrons (irrespective of energy they already possess) to absorb heat energy

49
Q

When is a body said to be free ?

A

When it is not under the influence of a force or a field

50
Q

Does a free body have energy ?

A

A free body at rest does not have any energy

51
Q

How is total energy calculated ?

A

It is the sum of kinetic energy (caused by motion) and potential energy(caused by position in field)

52
Q

In macroscopic situations, are there restrictions on the energy value a body is allowed to have ?

A

Only at velocities comparable to the velocity of light.

53
Q

Why ?

A

Relativity effects brings forth certain restrictions

54
Q

What is the potential energy of an electron in an atom caused by ?

A

It depends on the distance from the protons

55
Q

What is the kinetic energy of an electron in an atom cause by ?

A

Motion around the nucleus

56
Q

What happens when an electron of an atom receives energy ?

A

It goes to another orbit

57
Q

Can the energy levels of the orbits be anything ?

A

No, they are quantized

58
Q

Why does quantization of the energy of an electron occur ?

A

Because it is in the influence of the field due to a proton

59
Q

Does it apply to free electrons also ?

A

No, a free electron can have a continuous range of energy values

60
Q

What are the energy levels of an isolated atom like ?

A

They are discrete

61
Q

What happens when two atoms are bought close to each other ?

A

Each energy level gets split into two

62
Q

What happens when N atoms are bought close to each other (like they are in a solid) ?

A

Each energy level is split into N energy levels

63
Q

Does this mean that the energy values are now continuous ?

A

No, but they are practically continuous

64
Q

What is an energy band ?

A

A bunch of quasi-continuous energy levels

65
Q

What is a forbidden band or energy band gap ?

A

It is the energy band gap seperating two energy bands

66
Q

What is valence band ?

A

The band above which all bands are empty and below which all are occupied

67
Q

What is conduction band ?

A

The empty band above the valence band

68
Q

What is density of energy level ?

A

It is the number of permitted energy levels per unit energy range

69
Q

Why do we say density of energy STATES and not values ?

A

Each energy level is applicable to two energy states

70
Q

What are the two energy state ?

A

1 for spin-up, 1 for spin-down

71
Q

How is density of states g(E) defined ?

A

It is the number of energy states per unit energy range, centered at an energy E

72
Q

Which band is density of states defined in ?

A

The valence band of the material

73
Q

Why do we consider g(E) for a centered energy E ?

A

It is because there are a large number of permitted values. The density of energy level varies with energy in the band

74
Q

Are there any other conditions for defining g(E) ?

A

It is calculated at constant volume.

75
Q

What is Fermi level ?

A

The highest occupied level at zero degree absolute temperature

76
Q

What is Fermi energy level ?

A

It is the energy corresponding to that

77
Q

Why is it defined for zero degree absolute temperature ?

A

Because there is on external energy supply for the electrons at zero degree Kelvin.

78
Q

What is Fermi factor ?

A

It is the probability of occupation of a given energy state for a material in thermal equilibrium

79
Q

What is Fermi temperature ?

A

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
Q

What is Fermi velocity ?

A

The velocity of electrons which occupy Fermi level

81
Q

Why do free electrons move in metals ?

A

Applied Electric field + Periodic potential due to lattice ions

82
Q

What is effective mass of an electron ?

A

It is the mass the electron APPEARS to have

83
Q

How is it different from the true mass ?

A

The true mass is the mass the electron would have if there was an external field alone.

84
Q

What are the requirements of a perfect conductor ?

A

Infinite Conductivity

Infinite Collision Time

85
Q

How can collision time be made infinity ?

A

Scattering of electrons should vanish

86
Q

What are the main reasons for electron scattering ?

A

Lattice distortions

Lattice vibrations

87
Q

Why do lattice vibrations persist even at zero degree absolute temperature ?

A

According to the uncertainty principle, certain vibrations persist. It is called zero point vibration.

88
Q

Can perfect conductors be realised, even theoretically ?

A

No.

89
Q

How are perfect conductors defined ?

A

Conductivity TENDS to infinity

Collision time TENDS to infinity

90
Q

Are perfect conductors the same as super conductors ?

A

No

Physics (Second Semester) (6 decks)

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