Quantum Mechanical Atom Part II: Bohr vs Quantum Mechanical Atom Part II: Bohr vs. Schroedinger Chapter 8 Approximately Sections 2 thru 9 of Jespersen 6TH ed) Dr. C. Yau Spring 2013 1

Dual Nature of the Electron The e- behaves as a particle (matter, with mass)…classical physics. It also behaves as a light wave (non-matter, without mass and with wave properties) …quantum physics. De Broglie Wavelength (see lecture notes)

Heisenberg's Uncertainty Principle Δx Δv Δx = uncertainty in locating the electron Δv = uncertainty in measuring the velocity (velocity is speed with specified direction) h, 4,  and m are constants. Δx and Δv are inversely proportional. If Δx is small, (we can locate the e- accurately) then Δv must be large (we cannot determine the direction it is traveling.)

Heisenberg's Uncertainty Principle Δx Δv If Δv is small , (we can determine its direction) then Δx must be large (we cannot determine its location.) Significance: We cannot accurately determine the location AND the direction an electron is traveling simultaneously. We can never determine the pathway of the electron….we cannot say it "orbits"!

Why Schroedinger has to come up with a different model: Heisenberg's Uncertainty Principle. Bohr’s theory could predict emission lines for one electron system ONLY. What are one-electron systems? How is Schroedinger’s model different from Bohr’s? 5

Bohr's Planetary Model of the Atom 1. e- orbits like a planet around the sun. 2. E levels of the e- are quantized. 3. e- behaves as a particle. Schroedinger's Quantum Mechanical Model of the Atom 1. e- is found in orbitals. 2. E levels are quantized, but there are sublevels within. 3. e- behaves as a wave as well.

Orbit vs. Orbital Heisenberg's Uncertainty Principle tells us we cannot determine the pathway of the electron. We cannot say that it "orbits" like a planet around the sun. We can only talk about the probability of finding an electron in a certain location. An orbital is a shaped space surrounding the nucleus of the atom where a particular electron can be found 95% of the time. An orbit is a pathway. An orbital is not a pathway.

Schroedinger's Sublevels vs. Bohr's E levels Within Bohr's energy level (n), sublevels are… s, p, d, f, g, h, i…etc. These are orbitals of different shapes. There are limits to the number & type of orbitals allowed for the various n. (see lecture notes) To see the various shapes, try out this link! http://winter.group.shef.ac.uk/orbitron/AOs/1s/index.html

Schroedinger’s Equation ψ = wave function that describes an electron ψ2 = probability of finding an electron in specified location. (It tells us the shape of the orbital.) By solving this equation, Schroedinger came up with 4 quantum numbers to describe each electron in an atom. 9

The Set of 4 Quantum Numbers Principal quantum number = n Angular momentum quantum number =l Magnetic quantum number = ml Electron spin quantum number = ms Each electron in an atom has its own, unique set of 4 quantum numbers. No two electron in an atom can have the same set of quantum numbers. 10

Review of E Diagram of the Atom Bohr’s energy level n = Schroedinger’s principal quantum number n Quantum Mechanical Model has sub-levels within the principal energy levels, n. We can visualize this model by thinking of renting rooms in apartment buildings, and wishing to start with the lowest rent possible. (See lecture notes and handout.) 11

Rules of Filling Electrons into the E Diagram Aufbau Principle: Placing electrons into orbitals of the lowest energy first. Hund’s Rule: If there are more than one orbital of the same energy, electrons prefer to spread out first before pairing up. Pauli Exclusion Principle: An orbital can accommodate one or two electrons. When there are 2 electrons, they MUST be of different spins. 12