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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.
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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 probabilityof 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
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%.
The Quantum-Mechanical Model:Quantum Numbers • The Principal QuantumNumber, 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.
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 • psubshells have 3 orbitals • dsubshells have 5 orbitals • fsubshells 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
6d 7s 5f 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p 2s 1s Energy
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.
Unoccupied orbital Orbital with 1 electron Orbital with 2 electrons 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.
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.
