28'8 Electron Clouds and Orbitals

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28.8 Electron Clouds and Orbitals

• The graph shows the solution to the wave equation
  for hydrogen in the ground state
• The curve peaks at the Bohr radius
• The electron is not confined to a particular
  orbital distance from the nucleus
• The probability of finding the electron at the
  Bohr radius is a maximum

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Electron Clouds, cont

• The wave function for hydrogen in the ground
  state is symmetric
• The electron can be found in a spherical region
  surrounding the nucleus
• The result is interpreted by viewing the electron
  as a cloud surrounding the nucleus
• The densest regions of the cloud represent the
  highest probability for finding the electron

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Electron Clouds, final

• The boundary surfaces of p orbitals. The nodal
  plane passes through the nucleus and separates
  the two lobes of each orbital. The shaded areas
  denote regions of opposite sign of the
  wavefunction

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28.9 The Pauli Exclusion Principle

• No two electrons in an atom can ever be in the
  same quantum state
• In other words, no two electrons in the same atom
  can have exactly the same values for n, l, ml,
  and ms
• This explains the electronic structure of complex
  atoms as a succession of filled energy levels
  with different quantum numbers

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The Periodic Table

• The outermost electrons are primarily responsible
  for the chemical properties of the atom
• Mendeleev arranged the elements according to
  their atomic masses and chemical similarities
• The electronic configuration of the elements
  explained by quantum numbers and Paulis
  Exclusion Principle explains the configuration

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The Periodic Table, cont.

• The periodic table represents the ground state of
  the atoms. The electrons fill the available
  energy levels from the bottom up, that is, from
  the lowest to the highest energy, consistent with
  Paulis exclusion principle. The picture shows
  the procedure for the five most simple atoms.

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The Periodic Table, final

• The number of electrons of the atom determines
  its position in the periodic table Hydrogen with
  one electron is on the first place, Helium with
  two electrons is on the second position, Lithium
  with three on the third position, etc.

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28.10 Characteristic X-Rays

• When a metal target is bombarded by high-energy
  electrons, x-rays are emitted
• The x-ray spectrum typically consists of a broad
  continuous spectrum and a series of sharp lines
• The lines are dependent on the metal
• The lines are called characteristic x-rays

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Explanation of Characteristic X-Rays

• The details of atomic structure can be used to
  explain characteristic x-rays
• A bombarding electron collides with an electron
  in the target metal that is in an inner shell
• If there is sufficient energy, the electron is
  removed from the target atom
• The vacancy created by the lost electron is
  filled by an electron falling to the vacancy from
  a higher energy level
• The transition is accompanied by the emission of
  a photon whose energy is equal to the difference
  between the two levels

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Energy of the X-ray

• Consider two electrons in the K shell of an atom
  whose atomic number is Z. Each electron partially
  shields the other from the charge of the
  nucleus, Ze, and so each is subject to an
  effective charge of Zeff(Z-1)e.
• EK-Zeff2E0-(Z-1)2(13.6 eV)

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Moseley Plot

• ? is the wavelength of the K? line
• K? is the line that is produced by an electron
  falling from the L shell to the K shell
• From this plot, Moseley was able to determine the
  Z values of other elements and produce a periodic
  chart in excellent agreement with the known
  chemical properties of the elements

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28.11 Atomic Transitions Energy Levels

• An atom may have many possible energy levels
• At ordinary temperatures, most of the atoms in a
  sample are in the ground state
• Only photons with energies corresponding to
  differences between energy levels can be absorbed

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Atomic Transitions Stimulated Absorption

• The blue dots represent electrons
• When a photon with energy ?E is absorbed, one
  electron jumps to a higher energy level
• These higher levels are called excited states
• ?E h E2 E1
• In general, ?E can be the difference between any
  two energy levels

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Atomic Transitions Spontaneous Emission

• Once an atom is in an excited state, there is a
  constant probability that it will jump back to a
  lower state by emitting a photon
• This process is called spontaneous emission

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Atomic Transitions Stimulated Emission

• An atom is in an excited state and a photon is
  incident on it
• The incoming photon increases the probability
  that the excited atom will return to the ground
  state
• There are two identical emitted photons, the
  incident one and the emitted one
• The emitted photon is exactly in phase with the
  incident photon

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Photon-Atom Interactions, Summary
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28.12 Lasers

• Laser ? light amplification by stimulated
  emission of radiation

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How to build a Laser?

• (a) Pumping (energy input)
• (b) Cavity to make the pumping effective enough
• (c) Laser emission due to population inversion

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Population Inversion

• When light is incident on a system of atoms, both
  stimulated absorption and stimulated emission are
  equally probable
• Generally, a net absorption occurs since most
  atoms are in the ground state
• If you can cause more atoms to be in excited
  states, a net emission of photons can result
• This situation is called a population inversion

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Laser Conditions and Requirements

• A) Stimulated emission
• B) Population inversion (more stimulated emission
  than absorption)
• C) Cavity (to gain the stimulated emission)

Excited state full
Stimulated emission
Ground state empty
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Laser Beam Ruby Example
(a)
(b)
(a) Sketch of the first ruby laser. (b) The
energy levels.
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Holography

• Holography is the production of three-dimensional
  images of an object
• Light from a laser is split at B
• One beam reflects off the object and onto a
  photographic plate
• The other beam is diverged by Lens 2 and
  reflected by the mirrors before striking the film

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Holography, cont.

• The two beams form a complex interference pattern
  on the photographic film
• It can be produced only if the phase relationship
  of the two waves remains constant
• This is accomplished by using a laser
• The hologram records the intensity of the light
  and the phase difference between the reference
  beam and the scattered beam
• The image formed has a three-dimensional
  perspective

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28.13 Energy Bands in Solids

• In solids, the discrete energy levels of isolated
  atoms broaden into allowed energy bands separated
  by forbidden gaps
• The separation and the electron population of the
  highest bands determine whether the solid is a
  conductor, an insulator, or a semiconductor

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Energy Bands, Detail

• Sodium example
• Blue represents energy bands occupied by the
  sodium electrons when the atoms are in their
  ground states
• Gold represents energy bands that are empty
• White represents energy gaps
• Electrons can have any energy within the allowed
  bands
• Electrons cannot have energies in the gaps

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Energy Level, Definitions

• The valence band is the highest filled band
• The conduction band is the next higher empty band
• The energy gap has an energy, Eg, equal to the
  difference in energy between the top of the
  valence band and the bottom of the conduction band

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Conductors

• When a voltage is applied to a conductor, the
  electrons accelerate and gain energy
• In quantum terms, electron energies increase if
  there are a high number of unoccupied energy
  levels for the electron to jump to
• It takes very little energy for electrons to jump
  from the partially filled to one of the nearby
  empty states

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Insulators

• The valence band is completely full of electrons
• A large band gap separates the valence and
  conduction bands
• A large amount of energy is needed for an
  electron to be able to jump from the valence to
  the conduction band
• The minimum required energy is Eg

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Semiconductors
Electrons

• A semiconductor has a small energy gap
• Thermally excited electrons have enough energy to
  cross the band gap
• The resistivity of semiconductors decreases with
  increases in temperature
• The white area in the valence band represents
  holes

Holes
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Semiconductors, cont.

• Holes are empty states in the valence band
  created by electrons that have jumped to the
  conduction band
• It is common to view the conduction process in
  the valence band as a flow of positive holes
  toward the negative electrode applied to the
  semiconductor

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Current Process in Semiconductors

• An external voltage is supplied
• Electrons move toward the positive electrode
• Holes move toward the negative electrode
• There is a symmetrical current process in a
  semiconductor

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Doping in Semiconductors

• Doping is the adding of impurities to a
  semiconductor
• Generally about 1 impurity atom per 107
  semiconductor atoms
• Doping results in both the band structure and the
  resistivity being changed

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n-type Semiconductors

• Donor atoms are doping materials that contain one
  more electron than the semiconductor material
• This creates an essentially free electron with an
  energy level in the energy gap, just below the
  conduction band
• Only a small amount of thermal energy is needed
  to cause this electron to move into the
  conduction band

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p-type Semiconductors

• Acceptor atoms are doping materials that contain
  one less electron than the semiconductor material
• A hole is left where the missing electron would
  be
• The energy level of the hole lies in the energy
  gap, just above the valence band
• An electron from the valence band has enough
  thermal energy to fill this impurity level,
  leaving behind a hole in the valence band

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28.14 p-n Junction

• A p-n junction is formed when a p-type
  semiconductor is joined to an n-type
• Three distinct regions exist
• p region
• n region
• Depletion region

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The Depletion Region

• Mobile donor electrons from the n-side nearest
  the junction diffuse to the p-side, leaving
  behind immobile positive ions
• At the same time, holes from the p-side nearest
  the junction diffuse to the n-side and leave
  behind a region of fixed negative ions
• The resulting depletion region is depleted of
  mobile charge carriers
• There is also an internal electric field in this
  region that sweeps out mobile charge carriers to
  keep the region truly depleted and to prevent
  further diffusion

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Diode Action

• The p-n junction has the ability to effectively
  pass current in only one direction
• When the p-side is connected to a positive
  terminal, the device is forward biased and
  current flows
• When the n-side is connected to the positive
  terminal, the device is reverse biased and a
  very small reverse current results

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Applications of Semiconductor Diodes

• Rectifiers
• Change AC voltage to DC voltage
• A half-wave rectifier allows current to flow
  during half the AC cycle
• A full-wave rectifier rectifies both halves of
  the AC cycle
• Transistors
• Electronic amplifier for small signals
• Integrated circuit
• A collection of interconnected transistors,
  diodes, resistors and capacitors fabricated on a
  single piece of silicon