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![[Post New]](/templates/default/images/icon_minipost_new.gif) 24 Apr 2007 12:28:17 IST
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Energy Structure of Solids - A solid is a 3-d array of vast numbers of atoms or ions linked in crystalline structure
- valence electrons are far from nucleus
- can be detached from the atom if enough energy supplied
- free to move through crystal
- Properties depend on how tightly bound electrons are in crystal
Insulators - electrons tightly bound to host ion
- need large amounts of energy to break free
- low numbers of free electrons
- electric currents do not pass easily
Metals - Electrons very loosely bound to host ions
- very easy to break free from ions
- free to "wander" around crystal
- large numbers high conductivity
- movement of electrons produces current in opposite direction
Semiconductors - Electrons have moderate binding energies
- at absolute zero, all electrons are tightly bound => insulator
- at very high temps, material can conduct => conductor
Conduction in metals - Free electrons in metal have a wide range of energies & velocities
- they behave as a "cloud" or "sea" of electrons
- individual electrons collide with ion cores as they drift through crystal
- individual electrons may travel in many different directions
- There is no net flow of current
- the flow in one direction is randomly balanced by the flow in another
- the average velocity of the electrons is zero
- The electron cloud can be accelerated by applied external electric-field
- this constitutes a potential difference being applied across the ends
- the electron cloud moves in opposite direction to field with drift velocity vd
- this constitutes an electric current in direction of field
Conduction of electrons in a metal - For n electrons/unit volume, the current flow through the conductor is (in the direction of the electric field)
I = total charge/unit time = - nqAl /t = - nqAv d The current density, is J = I/A = - nqv d The force on each electron under influence of applied E-field F = -qE But, F = m ea a = -qE/m e = v d/  where is average time between collisions Thus v d = -q E/m e Thus the current density J = nq 2E/m e Expressing conductivity as  = nq 2/m e We have the current density as | J = E | OHM's LAW | That the above equation is indeed a representation of Ohm's Law can be verified by substitution of E = V/ l, = 1/  , and J = I/A
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The Scientist does not study nature because it is useful; he studies it because he delights in it, & he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, life would not be worth living. Ofcourse I do not here speak of that beauty that strikes the senses, the beauty of qualities & appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmoniuos order of the parts, & which a pure intelligence can grasp. |
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