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Atomic Orbitals and Hybrid Orbitals

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Atomic Orbitals and Hybrid Orbitals Powered By Docstoc
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                  Uncertainty
 All measurements have a degree of uncertainty in
 them


      ocm      1cm        2cm       3cm

 We can tell that the blue bar is 2.3 cm for sure
   We can also estimate the next digit since the blue
    bar is clearly between the 3 and 4 mm mark, but
    this number is not 100% sure


 Therefore we say the blue bar is 2.35cm ± 0.02
    The 0.02 is the uncertainty in the measurement
  Heisenberg Uncertainty Principle
 How do we observe anything?
   We often use light that bounces off an object to
    determine its position and speed
   We do the same with particles


 It turns out that the higher energy (lower
 wavelength) light we use, the more accurately we can
 determine the position of a particle

 But we have learned that light can impart
 momentum on particles...
 Heisenberg Uncertainty Principle
 Since light imparts momentum on particles, the act
 of observing them causes their behaviour to change

 The more accurately we try to determine their
 position (by increasing the energy of the light) the
 more momentum we give the particles.
   Meaning we know their momentum less accurately


 Heisenberg determined that there is always a
 certain degree of uncertainty in our knowledge of the
 behaviour of particles
 Heisenberg Uncertainty Principle
 The product of the uncertainties in position (x) and
 momentum (p) must always be larger than a
 constant

                      ΔxΔp > h/4

 This means that even if we only think of electrons as
 particles, we can never truly know everything about
 what they are doing in an atom
   We must then think in probabilities
      Schrödinger Wave Equation
 A physicist named Erwin Schrödinger developed an
  equation that describes the states of electrons in
  atoms and can be used to properly predict the
  emission spectra of atoms

 It is based on Louis de Broglie’s work with electron
  waves and utilizes the idea of probability in
  describing the actions of electrons

 Ψ (psi) is the symbol for the wave function
   It represents the set of probabilities (ψ) that the atom
    exists in different states
      Schrödinger Wave Equation
 The electrons are viewed as standing waves, and
 have only specific energies in each orbit due to their
 wavelength




 The atom can exist in many different states, with the
 electron in many different orbitals
      Schrödinger Wave Equation
 The atom is said to simultaneously exist in all of the
 possible states until one specific state “condenses”
   This idea is not very well understood, but it leads to
    interesting technology like touch screens

 The idea of states existing simultaneously is called
 “superposition”

 The superposition of states has famously been
 described using the “Schrödinger’s Cat” paradox
                   Schrödinger’s Cat



Hammer
 Fuzzy Cat

Geiger Counter

Poisonous Gas


Radioactive Material
                Schrödinger’s Cat
 There is a 50% chance the radioactive material will
 decay in 1 hour and a 50% chance that it will not
   Meaning for that hour there is an equal chance that the
    cat is alive or dead – and we do not know which is true

   For that hour we say that the cat is
    both alive and the dead

   The state condenses into one or the
    other when we open the box and
    make an observation
               Electron Clouds
 Since we can’t know everything about the actions
 of electrons, we view orbitals as clouds of negative
 charge
   Each point in the orbital has a certain probability
    that the electron will be there at any given moment
    in time
 We picture orbitals as clouds of electron density
                 Atomic Orbitals
 If the electron density of different orbital types (s, p,
 d, f) are graphed and modeled, we see that each type
 has its own characteristic shape
   We can also see the differences between the degenerate
    orbitals


 Degenerate orbitals often look similar but are
 arranged differently in space

 3D Representations
Atomic Orbitals
             Electron Density
Atomic Orbitals
                Atomic Orbitals
 As n increases, the number of nodes in an orbital
 increases
   A node is a region where there is zero electron density
   Ex: 1s – 0 nodes, 2s – 1 node, 3s – 2 nodes etc.


 As l increases, the number of nodes decreases
   3s – 2 nodes, 3p – 1 node, 3d – 0 nodes
            Quantum Tunnelling
 Using the probabilistic approach to viewing matter,
 every particle has a probability of existing anywhere
   But most of these probabilities are extremely small


 This can be used however to transport particles
 through and across barriers
   Ex: an alpha particle (helium nucleus) within a larger
    nucleus (like Ra) has a small probability of existing
    outside of the nucleus
   This is how radioactive decay occurs
                 Ra-226  Rn-222 + He
           Quantum Tunnelling
 Quantum tunnelling is also the phenomenon behind
 touch screens

 The electrons in the screen have a small probability
 of being located in the sensors below the screen.
   As the screen is pushed and the screen moves closer
    the sensors beneath, the probability increases
   Eventually the probability is large enough that a
    significant (though small) number of electrons “jumps”
    from the screen to the sensors and starts an electric
    current

				
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