QMM Model Mr. Matthew Totaro Legacy High School Honors Chemistry

Problems with the Bohr Model The Bohr model could only predict the emission spectrum for hydrogen. The Bohr model failed to predict the emission spectra for all of the other elements. The Bohr model did not take into account the fact that electrons repel each other, thus causing shifts in the lines in the spectra.

The Quantum-Mechanical Model of the Atom Erwin Schrödinger applied the mathematics of probability and the ideas of quantizing energy to the physics equations that describe waves, resulting in an equation that predicts the probability of finding an electron with a particular amount of energy at a particular location in the atom. Erwin Schrodinger

The Quantum-Mechanical Model of the Atom: the Schrodinger Equation

Probability Maps and Orbital Shape

The Quantum-Mechanical Model: Orbitals The result is a map of regions in the atom that have a particular probability for finding the electron. An orbital is a region where we have a very high probability of finding the electron when it has a particular amount of energy. Generally set at 90 or 95%.

Orbits vs. Orbitals Pathways vs. Probability

The Quantum-Mechanical Model: Quantum Numbers The Principal Quantum Number, n, specifies the energy level for the orbital. The number of electrons in each principal quantum number still follows the 2n2 rule.

The Quantum-Mechanical Model: Subshells Each principal energy level (shell) has one or more sublevels (subshells). The number of subshells = the principal quantum number. Each subshell is designated by a letter. s, p, d, f. Each kind of subshell has orbitals with a particular shape. The shape represents the probability map. 90% probability of finding electron in that region.

s Orbitals

p Orbitals

d Orbitals

f Orbitals

Shells and Subshells

The Number of Sublevels on an Energy Level The number of subshells on an energy level can be calculated by the n2 rule. n = the principal energy level number. 1st energy level = (1)2 = 1 orbital (s only) 2nd energy level = (2)2 = 4 orbitals (s + p) 3rd energy level = (3)2 = 9 orbitals (s + p + d)

Subshells and Orbitals The subshells of a principal shell have slightly different energies. s < p < d < f. Each subshell contains one or more orbitals: s subshells have 1 orbital p subshells have 3 orbitals d subshells have 5 orbitals f subshells have 7 orbitals

Electron Configurations The distribution of electrons into the various energy shells and subshells in an atom in its ground state is called its electron configuration. Each energy shell and subshell has a maximum number of electrons it can hold (1 orbital = 2 e-). s = 2, p = 6, d = 10, f = 14. Aufbau principle: place electrons in the shells and subshells in order of energy, from low to high

6s 6p 6d 7s 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d Energy 2s 2p 1s

Practice —Write an electron configuration for Potassium (K)

Filling an Orbital with Electrons Pauli Exclusion principle: Each orbital may have a maximum of 2 electrons with opposite spins. Electrons spin on an axis. Generating their own magnetic field. When two electrons are in the same orbital, they must have opposite spins. So their magnetic fields will cancel.

Electron Spin

Orbital Diagrams We often represent an orbital as a square and the electrons in that orbital as arrows. The direction of the arrow represents the spin of the electron. Unoccupied orbital Orbital with 1 electron Orbital with 2 electrons

Filling an Orbital with Electrons Hund’s rule: When filling orbitals that have the same energy, place one electron in each before completing pairs and they must have the same spin.

Practice —Write an Orbital Diagram for Potassium (K)