Electrons as waves

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Electrons as waves

• Scientists accepted the fact that light has a
  dual wave- particle nature.
• De Broglie pointed out that in many ways the
  behavior of the Bohrs quantized electron orbits
  was similar to the known behavior of waves.
• Electrons should be thought of as having a dual
  wave-particle nature also.

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Evidence Electrons

• Electron beams could be diffracted or bent.
• Electron beams demonstrated the properties of
  interference.

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Heisenberg Uncertainty Principle

• Werner Heisenberg (1927)
• It is impossible to determine simultaneously both
  the position, and velocity, of an electron or any
  other particle.

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Heisenberg explained

• To locate an object you would have to be able to
  look at it.
• When we see an object we actually are seeing the
  light waves that the object reflects.
• For us to see an object a photon of light has to
  hit it.

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Heisenberg explained

• A photon hitting a book or an airplane has no
  noticeable affect.
• However, an electron is so small that once a
  photon its it, the electron undergoes a large
  energy change and is moved.
• Similarly, the collision between the photon and
  the electron causes the electrons velocity to
  change.

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In summary

• If we were able to measure the location, the
  velocity would change
• If we were to measure the velocity, the location
  will change.
• Note Treats electron like a particle

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Schrodinger s wave equation

• Developed an equation that treats electrons as
  waves. ( related the amplitude of the electron
  wave to any point in space around the nucleus).

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Quantum theory

• Heisenbergs uncertainty principle and
  Schrodingers equation laid the foundation for
  quantum theory.
• Quantum theory- describes mathematically the wave
  properties of electrons and other very small
  particles.

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Probability

• Ceiling fan- where are the blades at any one
  moment?

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Orbital

• Three dimensional region around the nucleus that
  indicates the probable location of an electron.
• These three dimensional shapes are named s, p, d,
  and f.
• When describing the location of the electrons
  in an orbital we are indicating that there is a
  99 chance that the electron will be found there.

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Quantum numbers

• A list of three numbers that describe the
  location of the electron
• The numbers represent
• The main energy level
• The shape
• The orientation of the orbital, axis

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Spin of electron

• A fourth number indicates the spin within the
  orbital.

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Principle quantum number

• 1-7 representing the energy level
• Symbolized by the letter n
• As n increases the distance from the nucleus
  increases
• As n increases the potential energy of the
  electron increases.

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Angular momentum or orbitals

• The different shaped orbitals are also called
  sublevels.
• Symbolized by l, indicates the shape of the
  orbital
• 2 electrons are allowed in one orbital
• The number of orbital shapes, l, possible is
  equal to n ( up to n4)

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continued

• The values of l allowed are 0 and all possible
  integers up to n-1
• l n-1
• 0 s shape
• 1 p shape
• 2 d shape
• 3 f shape

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2 electrons per orbital

• The s shape has 1 orbital total of 2 electrons
• The p shape has 3 orbitals 6 electrons
• The d shape has 5 orbitals 10 electrons
• The f shape has 7 orbitals 14 electrons
• See page 103
• Each orbital is on a different axis, ( x,y,z etc.
  )

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Magnetic quantum number

• Indicates the orientation of the orbital around
  the nucleus.
• Symbolized by the letter m
• Indicated by numbers on either side of zero
• The s shape has an m value of 0 ( no axis)
• The p shape has m values of 1,0,1
• The d shape has m values of 2,-1,0,1,2

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Summary

• n,l,m
• Energy level, shape, axis

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SpinThe last number is a spin indicator

• -1/2 or ½
• These are the two spin states, ( spin to the
  right or spin to the left)
• No two electrons can be identical., or , no two
  electrons can have the same set of quantum
  numbers Paulis exclusion principle
• A maximum of two electrons can occupy an orbital,
  each will have a different spin.

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Mathematical equations

• The number of orbitals per energy level is n2
• n2, there are 4 orbitals 1 s and 3 p
• n3 there are 9 orbitals 1s, 3p, 5d

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Number of electrons

• Since there are 2 electrons per orbital
• 2n2 is the number of electrons per energy level.

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