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Quantum Mechanics  The application of quantum theory to explain the properties of matter, particularly electrons in atoms

Schrodinger’s Standing Waves  Louis De Broglie developed a theory that matter can have wave-like properties  Schrodinger extended this theory to electrons bound to a nucleus  Postulated that electrons resembled a standing wave  Certain orbitals exist at whole wavelengths of electron vibrations

Orbitals - Redefined  Orbital: region around the nucleus where there is a high probability of finding an electron  As per wave model of Schrodinger – because things are vibrating

Heisenberg Uncertainty Principle

 Heisenberg studied statistics and developed matrix algebra  Developed a statistical approach to explaining how electrons works and realized…  IT IS IMPOSSIBLE TO KNOW THE EXACT POSITION AND SPEED OF ELECTRON AT A GIVEN TIME  At best, we can describe the probability of finding it at a specific place

 Wave functions: the mathematical probability of finding an electron in a certain region of space  Wave functions give us:  Electron probability densities: the probability of finding an electron at a given location, derived from wave equations

Homework

Quantum Numbers  Quantum Numbers: numbers that describe the quantum mechanical properties (energies) of orbitals  From the solutions to Schrodinger’s equation  The most stable energy states is called the ground state

Principal Quantum Number (n)  Integer number (n) used to level the main shell or energy level of the electron  Describes size and energy of the atomic orbital  Increase number = increase energy, bigger

Secondary Quantum Number, l  Describes the shape of the orbital within each shell  Each energy level contains several sublevels  Relates to the shape of the orbital  Can be any integer from 0 to (n-1)

Values of l Value01234 Letter Used spdfg Namesharpprincipaldiffusefundamental

 Each orbital is given a code:  Example  If n = 1, l = 0 then we call it a 1s orbital  If n = 3, l = 2 then we call it a 3d orbital

Magnetic Quantum Number, m l  Describes the orientation of the orbital in 3- space  Can be whole number integers from – l to + l  Example: if l = 1, then m l can be -1, 0, +1  There are 3 possible p orbitals  p x, p y, and p z

 What are possible values for m l if l is:  0  1  2  3

Spin Quantum Number  Electrons are basically little magnetics spin around when placed in magnetic fields, they can have spin ‘up’ or spin ‘down’  m s can be either +1/2 or – 1/2

Homework

Electron Configurations and Energy Level Diagrams  The four quantum numbers tell us about the energies of electrons in each atom  Unless otherwise stated were are talking about ground state energies

Energy Diagrams  Describe how electrons fill orbitals using quantum numbers  Electrons fill the lowest energy level orbitals first  Each shell is (for the most part) filled before moving to higher shells

Rules  Use circles (or boxes) to represent each orbital in any given energy level and arrows for electrons  Unoccupied circles imply that there are no electrons in it  A circle can have at most two electrons in it; only if the arrows are pointing in opposite directions

Rules to Remember  Pauli exclusion Principle: no two electrons can have the same 4 quantum numbers. Electrons in the same orbital can’t have the same spin  Hund’s Rule: One electron occupies each of sub-orbitals in the same energy level before a second can occupy the same sub-orbital  Aufbau Principle: each electron is added to the lowest energy orbital available

Building Orbital Diagrams

Practice  H, B, C, Ne  Mg, P, Ar  Ca, Mn, Zn, Ge, Kr

Electron Configurations  Condensed versions of orbital diagrams  Write the electron configuration for each of the atoms above

Exceptions to the Rules  Examine the allowed charges for Chromium and Copper  Write the electron configuration for chromium and copper

What actually happens?  Why? Evidence suggests that half-filled and filled orbitals are more stable than other orbitals, so electrons rearrange to give these configurations

Explaining Ion Charges  In order to get particular charges, entire energy levels or sublevels get cleared first.  Use electron configuration theory to explain why:  Zn  Zn 2+  Pb  Pb 2+ or Pb 4+

Explaining Trends in the Periodic Table  Atomic Radius: size of the atom  Ionization Energy: energy needed to remove an electron from the outermost energy level from an electron in the gaseous state  Electron Affinity: change in energy that occurs when an electron is added to a gaseous atom