Unformatted text preview: Molecularity Molecularity CH1010
Chapter 7 Part III Quantum Theory and Atomic Structure James P. Dittami WaveGenerating Apparatus WaveGenerating Apparatus A Standing Wave Electrons and Standing Waves Electrons and Standing Waves Electrons can be wavelike and restricted to orbits of fixed radii around nucleus Heisenberg Heisenberg Particles have definite location Waves are spread out in space Electrons have properties of both Can we define their position and momentum? No you can know a particle is here now but can’t say where it will be an instant later. Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle
Attempting to measure an elementary particle’s position to the highest degree of accuracy, leads to an increasing uncertainty in being able to measure the particle’s momentum to an equally high degree of accuracy. ∆ x • m∆ u ≥ h/4π For a particle of constant mass m where ∆ x = uncertainty in position and ∆ u = the uncertainty in speed (a smaller number for ∆ x or ∆ u = higher accuracy) What does this tell us? Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle
“The product of the uncertainties in two simultaneous measurements cannot be less than a certain constant value”* ∆ x • m∆ u ≥ h/4π So if ∆ x = uncertainty in position is small (high accuracy) then ∆ u = the uncertainty in speed must be large (low acccuracy) and visa versa, Conclusion: It is impossible to know the exact position and momentum (m x v) at any given instant. “Chemical Principles”, by Peter Atkins and Loretta Jones, Freeman Press 4th Edition Uncertainty Principle Uncertainty Principle We cannot know both position and momentum of e So we cannot assign fixed paths or trajectories for the electrons orbits We can only talk about the probability of finding an electron somewhere This leaves us with the idea of orbitals the areas around the nucleus where we are likely to see the electron WaveGenerating Apparatus WaveGenerating Apparatus A Standing Wave Quantum Mechanics Quantum Mechanics Heisenberg, De Broglie and Schrödinger Bohr’s model was lacking Consider the electron as a standing wave Do Probability Distributions or Wave Functions Mathematical attempts to describe where the electron is at any given time. No information about detailed pathway of the electron Only on where we are likely to find it. The Schrödinger Equation The Schr Η Ψ =E Ψ Ψ is a wave function It describes the electron’s position in 3d space. H is the Hamiltonian Operator it represents a set of mathematical operations that carried out on Ψ yield an allowable energy value The Schrödinger Equation The Schr Each solution gives rise to an atomic orbital Although the wave function (atomic orbital) has no direct physical meaning Ψ2 or the square of the wave function gives a probability density – the probability of finding the electron in a particular volume of the atom The Schrödinger Equation The Schr For a given Energy level we can draw a Probability density diagram or Electron Density Diagram The Schrödinger Equation The Schr Hydrogen Predicts the electron in ground state H will most probably be found 5.29 x 102 nm or 0.529 Angstroms from the nucleus. Bohr postulated this distance for the orbit where the electron is all the time Quantum Mechanics says it will be found most of the time (90%) at this distance Quantum Numbers Quantum Numbers Three numbers that arise out of the Schrödinger Equation which describe Orbital Energy and Size Orbital Shape Orbital Orientation Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers.
n l the principal quantum number - a positive integer the angular momentum quantum number - an integer from 0 to n-1 the magnetic moment quantum number - an integer from -l to +l ml Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Principal, n Positive integer (size, energy) (1, 2, 3, ...) Quantum Numbers 1 2 3 Angular momentum, l 0 to n-1 (shape) 0 0 1 0 1 2 Magnetic, ml -l,…,0,…,+l (orientation) 0 0 -1 0 +1 0 -1 0 +1 -2 -1 0 +1 +2 Orbital Names and Shapes Orbital Names and Shapes An atoms Energy Levels or shells are given by the letter n The smaller the value the lower the energy The lower the energy the greater the probability of finding the electron there Orbital Names and Shapes Orbital Names and Shapes Within a Level n is a subshell of orbitals corresponding to different values of l l = 0 is an s Orbital l = 1 is a p Orbital l = 2 is a d Orbital l = 3 is a f Orbital Orbital Names and Shapes Orbital Names and Shapes The letters of the sublevels correspond to names For l values greater than 3 the levels are alphabetical g sublevel, h sublevel etc. s sharp p principal d diffuse f fundamental Orbital Names and Shapes Orbital Names and Shapes The Sublevels are named by joining the n value and the letter designation for the l sublevel For n = 4 l = 0 is a 4s Orbital l = 1 is a 4p Orbital l = 2 is a 4d Orbital l = 3 is a 4f Orbital Two Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals (a) The Electron Probability Distribution (b) The Surface Contains 90% of the Total Electron Probability (the Size of the Oribital, by Definition) Representation of the 2p Orbitals (a) The Electron Representation of the 2p Orbitals (a) The Electron Probability Distribution for a 2p Oribtal (b) The Boundary Surface Representations of all Three 2p Orbitals POrbitals px, py, pz POrbitals px, py, pz Representation of the 3d Orbitals (a) Representation of the 3d Orbitals (a) Electron Density Plots of Selected 3d Orbitals (b) The Boundary Surfaces of All of the 3d Orbitals Representation of the 4f Orbitals in Terms of Representation of the 4f Orbitals in Terms of Their Boundary Surfaces Figure 7.18 Orbital Energy Figure 7.18 Orbital Energy Levels for the Hydrogen Atom Figure 7.19 A Picture of the Figure 7.19 A Picture of the Spinning Electron The Orders of the Energies of the Orbitals in The Orders of the Energies of the Orbitals in the First Three Levels of Polyelectronic Atoms ...
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