The Quantum Mechanical Model of the Atom = model in which e- are treated as having wave characteristics

With Bohr’s model, so far we’ve been able to explain Atomic line spectra Atomic line spectra Energy states within the atom Energy states within the atom Still haven’t explained:  What the e- is doing inside the atom  Where the e- spend their time  Complex line spectra of multi-e- atoms

Wave-particle duality of Electrons Light has been regarded as having wave- particle duality. Light has been regarded as having wave- particle duality. Waves: a continuous traveling disturbance Waves: a continuous traveling disturbance Particles: discrete bundles Particles: discrete bundles Distinctions appear to break down on the atomic level. Distinctions appear to break down on the atomic level.

Louie de Broglie & Matter Waves If waves behave like particles, then particles should be able to behave like waves. If waves behave like particles, then particles should be able to behave like waves. The wavelength for particles should be: The wavelength for particles should be: Where Where h = Planck’s constant, m = the mass of the particle υ = the speed of the particle

Applying De Broglie equation: Calculate the wavelength of a 60-kg sprinter running at 10 m/s. Too small to be detected

The wave character of e- led to useful application of electron microscope in 1933 Dust mites

Erwin Schrödinger - Wave equation (1926) A wave theory and equations required to fully explain matter waves. An equation with 2 unknowns: E = allowed energy level of atom = wavefunction; a mathematical description of the electron H= the “hamiltonian”; not a variable, a set of mathematical instructions to be performed on Called psi

Only certain Energy values will result in answers (wavefunctions), Only certain Energy values will result in answers (wavefunctions), | 2 | Plotting | 2 | enables us to “see” the electron orbital Schrödinger equation Looks like Fun!!! An atomic orbital can be visualized as a fuzzy cloud where the electron is most likely to be at a given energy level

Orbitals: 2 for E 1 (n=1) plotted in 3-D A few notes: 2 is large near the nucleus  meaning e- most likely found in this region Value of 2 decreases as distance form nucleus increases, but 2 never goes to zero  probability of finding e- far from nucleus is small Also means an atom doesn’t have a definite boundary, unlike the Bohr model  Both are orbitals  probability density probability surface (≥95% probability)

Heisenberg’s Uncertainty Principle It is impossible to determine simultaneously the exact position and momentum of a single atomic particle  x  mv > h/4  Uncertainty in position Uncertainty in momentum Planck’s constant (6.626 x J s ) We cannot know the exact position of the electron; only where the electron is most likely to be. Werner Heisenberg

Quantum Numbers: n, l, m l, m s A set of 4 quantum numbers give information about each orbital and each electron Tell us the characteristics of the electron waveforms

So, this picture we’ve learnt from grade 9 is no longer correct The most recent, accepted model of an atom looks like this

Watch Quantum mechanic short clip A beautiful amalgamation of the quantum mechanical model of atom