Quantum Mechanics

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Quantum Mechanics

• Chapter 4
• CPS Chemistry

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Objectives

• Discuss the wave-particle nature of light
• Describe the photoelectric effect
• Discuss how electrons act as waves
• Discuss the development of the quantum model of
  the atom
• What is Heisenberg Uncertainly principle
• Who was Schrodinger?

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Light as a Particle

• Visible light is a kind of electromagnetic
  radiation that exhibits wave like behavior as it
  moves through space.
• All electromagnetic radiation moves at the same
  speed in a vacuum 3.0x108m/s(speed of light)

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Photoelectric Effect

• Albert Einstein found that if you shined light on
  a piece of metal with the correct frequency that
  electrons would be knocked off, creating an
  electric current. Which could be detected like
  voltage flowing from a battery
• This is called the Photoelectric Effect, which
  Albert Einstein won the Nobel Prize for in 1921
• Note Nobel Prizes can be awarded years or
  decades after important discoveries have been made

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Quantum

• Max Plank found in the early 1900s that the
  release of light by hot objects (think filament
  in a light bulb) does not release energy in a
  stream (think water from a hose), but in small
  packets of energy (think the energy to throw a
  tennis ball) called Quanta (plural)
• A quantum is the minimum quantity of energy that
  can be lost or gained by an atom(energy needed to
  throw 1 tennis ball)

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Quantum II

• The vehicle for this energy is called a Photon, a
  mass-less particle of electromagnetic radiation
  (Think, tennis ball)

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Ground Excited states

• Electrons exist at certain levels outside the
  nucleus of the atom, the further away from the
  nucleus the higher the energy
• When a electron goes from an excited state
  (higher level) to a lower level, it releases
  energy in form of a photon, or light, each
  element has its own signature or frequency of
  light. It is this color(s) of light that allow us
  to identify different elements
• To get an electron to leave a ground state to go
  to a higher state you must add energy

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Electrons as Waves

• So far we have discussed how light can act as a
  particle, but conversely particles can act as
  waves
• Work by deBroglie found that electrons around the
  nucleus of an atom exhibited wave behavior,
  acting at certain frequencies around the nucleus
• Further experiments proved more wavelike behavior
  such as a stream of electrons can be bent
  (diffracted), or that two electron beams can
  interfere with each other, just like water waves.

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Heisenburgs Experiment

• The idea that electrons sometimes acted like
  particles and other times acted like waves was
  very confusing for scientists.
• Werner Heisenburg had an experiment where he
  tried to detect the exact location of an electron
  by hitting them with photons (about the same
  energy as an electron) like pool balls on a pool
  table. But with this method it was hard to
  pinpoint the location of any particular electron,

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Heisenburg Uncertainty Principle

• Through his experiment Heisenburg found that it
  was impossible to know both the location AND the
  speed of any particular electron simultaneously

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Schrödinger Wave Equation

• Schrödinger found that only specific energies for
  electrons made them act like waves, not ALL
  energies.
• Schrodinger Heisenburgs work laid the
  foundation for modern quantum theory

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Atomic Orbitals Quantum Numbers

• First, you must think of an atom 3-dimensionally,
  that electrons live in not only an x-y space but
  also in a z direction
• Quantum numbers are the address of an electron
  in relation to the nucleus
• Each electron has an address of a unique
  combination of 4 quantum numbers

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Principle Quantum number - N

• N is the principle quantum number, it represents
  the energy level of the electron, or how far away
  it is from the nucleus
• N can be a positive integer, 1, 2, 3, etc.
• The bigger the number, the higher the energy and
  the further it is from the nucleus
• More than one electron can have the same N
  quantum number, if they are in the same Shell
  or level. The total number of orbitals in a shell
  is equal to N2

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Angular Momentum QN

• Angular Momentum describes the shape of the
  sublevels of the orbital
• L value tells you the shape of the orbital, the
  number of shapes possible is equal the principle
  QN
• Example
• When n 1, there is one shape (sphere)
• When n 2 there are two shapes (sphere
  dumbbell)
• When n 3 there are three shapes (sphere,
  dumbbell, and flower)

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Values of L

• L can be zero or any positive integer, example
  0,1,2,3, up to n-1
• So if n 2 than the possible values for L are 0
  and 1, since the highest value is n-1
• What if n4 what are the values of L?
• 0,1,2,3 since 3 N-1 4-1(3)
• Understand that quantum numbers explain where the
  likelihood of an electron to be, but due to
  Heisnburgs uncertainty principle we can not know
  exactly where a particular electron is at any
  given time.

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Shapes of L

• Each value of L corresponds to a different shape
  of the orbital, and each shape has its own
  identifying letter
• 0 is the s orbital and has a sphere shape
• 1 is the p orbital and has a dumbbell shape
  (three orientations x,y,z)
• 2 is the d orbital and has a flower shape and has
  many different orientations
• 3 is the f orbital and has a bizarre shapes that
  can not easily be described.

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Orientation of L

• The magnetic quantum number explains the
  orientation or the orbital around the nucleus
• For the s orbital there is only one orientation
• M 0
• For the p orbital there are 3 orientations
• M -1,0,1
• For the d orbital there are 5 orientations
• M -2,-1,0,1,2
• For the f orbital there are 7 orientations
• M -3,-2,-1,0,1,2,3

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Spin Quantum Number

• Lastly, electrons in their orbitals also spin,
  and the spin of the electron can be described in
  two ways 1/2 and 1/2
• An orbital can have at most 2 electrons,
  therefore they must have opposite spins

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Review of Quantum numbers

• N Principle, describing how far from nucleus.
  N1,2,3,4,etc.
• L Angular Momentum, describing the shape of the
  orbital. L 0,1,2,3n-1
• S,p,d,f
• M Magnetic, describing the orientation around
  the nucleus
• Sp Spin, either ½ or - ½
• Each electron needs a UNIQUE set of Quantum
  Numbers