FROM BOHR TO SCHROEDINGER Bohr Model Deficiencies Experimental: The calculated line spectra results for atoms with more electrons didn’t match observations. Spectral lines that couldn’t be accounted for Observed periodic structural trends in both valence level and electrons differed beyond Atomic Number 18. Bohr predicted 2n2 electrons per valence level 2, 8, 18, 32, 50 vs 2, 8, 8, 8

Theoretical: Equates position with energy and does not allow Potential and Kinetic Energy inter-conversion. The electron stays at the same distance from the nucleus, but doesn’t move? Fails to account for how electrons make energy (orbit) transitions if they are not permitted to be at any distance but the allowed orbit distance. The electron can’t “jump” creating line spectra, which is the basis of his theory.

Probability vs Probability Density The probability graph shows the most likely place to find the electron. But, it is not in the area closest to the nucleus.

The Scatter Diagram The probability graph doesn’t tell the whole story The scatter diagram of the stone tosses (electrons) shows that the density is actually close to the nucleus

Probability Density The area around the nucleus is smaller than the surrounding rings When the density of throws is graphed, it shows that the electron is actually as close to the nucleus as expected

PROBABILITY MODEL OR QUANTUM MECHANICS Electrons can be anywhere in their orbital, traveling in any direction with a certain, fixed total energy. As the electron travels, its PE and KE constantly exchange but the total electron energy remains fixed. Called the Principle Energy. Some locations about the nucleus are more probable than others.

Position and direction of travel may not be simultaneously known (Heisenberg Uncertainty Principle). An orbital is an equation solution to a more complicated equation called the Schroedinger Equation. To solve the Schroedinger Equation and generate orbital equations, four separate constants called Quantum Numbers must be assigned values. These assigned values identify the specific orbital. An orbital equation is its most probable physical location over a period of time as a 3D mapping or scatter diagram.

Scanning Tunnelling Microscopy (STM) SCH 4U1

STM Image of Graphite

STM Image of Quantum Corral Iron on Copper

STM of Two Electron Corral Iron on Copper

Quantum Numbers Each Bohr orbit is viewed as a Principle Energy Level defined by Principle Quantum Number, n where n = 1, 2, 3, 4.... Each Principle Energy Level contains “n” energy sub levels or orbital types defined by the Secondary or Orbital Quantum Number, l where l = 0 to n-1. n l = 0 l = 1 l = 2 l = 3 1 sharp 2 s principal 3 s p diffuse 4 s p d fundamental These 2 quantum numbers give the 1st 2 parts of an electron configuration. eg. 2s22p3

Orbitals for Electrons s, p, d, and f

Each Principle Energy Level contains a total of “n2” orbitals defined by their spatial orientation and the Magnetic Quantum Number, ml where -l ≤ ml ≤+l 1 of type s ml = 0 3 of type p ml = -1, 0, +1 these give the different orbital boxes -1 0 +1 5 of type d ml = -2, -1, 0, +1, +2 7 of type f ml = -3, -2, -1, 0, +1, +2, +3

The sublevels now explain the line spectra { { { { f s p d

Each orbital describes the behavior of two electrons at most, defined by the Spin Quantum Number, mS = +1/2 or -1/2 This gives the up and down arrows,  Now each electron has its own set of Quantum numbers. These numbers can be entered into the Schroedinger equation and the orbital for that electron can be mapped out and drawn We can also give the quantum numbers for any electron in an orbital box configuration.