Bulls-eye Activity

Did the pennies consistently drop in the same ring? Can we use our empirical evidence to predict exactly where a penny would land?

Quantum Mechanical Model of the Atom

Name This Element

Building on Bohr The simple Bohr model was unable to explain properties of complex atoms Only worked for hydrogen A more complex model was needed… Our understanding of physics needed to “catch up”

Wave Particle Duality Experimentally, DeBroglie found that light had both wave and particle properties Therefore DeBroglie assumed that any particle (including electrons) could also travel in waves Wavelengths must be quantized or they would cancel out Applied his theory to Bohr’s model and it fit, but still only for hydrogen Video

Heisenberg’s Uncertainty Principle Due to the wave and particle nature of matter, it is impossible to precisely predict both the position and momentum of an electron Δposition Δmv = a constant We can only describe a region of probability of finding an electron Video

Schr Ö dinger’s Wave Equation Schr Ö dinger’s developed a mathematical equation that could be used to determine a region of probability for finding an electron Substitute in a series of quantum numbers to solve the wave function His equation matched Bohr’s calculations including multi-electron atoms.

Quantum Mechanics Uses mathematical equations to describe the wave properties of subatomic particles It’s impossible to know both the exact position, momemtum of an electron (Heisenberg Uncertainty Principle) So Bohr’s “orbits” were replaced by orbitals –A wave function that predicts an electron’s energy and location within an atom –A probability cloud in which an electron is most likely to be found

OrbitsOrbitals - Bohr - 2-dimensional ring - Electron is a fixed distance from nucleus - 2, 8, or 18 electrons per orbit - Quantum Mechanics - 3-dimensional space - Electrons are a variable distance from nucleus - 2 electrons per orbital

Practice Problems Read p P. 202 #1-5 “Empirical Evidence supports theoretical knowledge”

Quantum Numbers Four numbers used to describe a specific electron in an atom Each electron has its own specific set of quantum numbers Recall: Describes orbitals (probability clouds)

The Principal Quantum Number “n” Indicates the average distance (size) of the orbital from the nucleus (same as Bohr’s energy levels) Higher n = greater distance from nucleus = greater energy n = integers > 1 (1,2,3…) The greatest number of electrons possible in each energy level is 2n 2

The Secondary Quantum Number “ℓ ” Describes the shape of the orbital Atoms with many electrons showed spectrum with many lines, some close together and others spaced apart Subshells within the main energy levels Each subshell has a different shape with the highest probability of finding an electron

The Secondary Quantum Number “ℓ ” Positive integers ranging from 0-3 Maximum value of n-1 –ℓ = 0 (s orbital) –ℓ = 1 (p orbital) –ℓ = 2 (d orbital) –ℓ = 3 (f orbital) Total number of sublevels = n

The Magnetic Quantum Number “m ℓ ” Describes orientation of the orbital m ℓ = integers from -ℓ to +ℓ Maximum number of orientations = n 2

Animation

The First Three Quantum Numbers

The Spin Quantum Number “m s ” Describes the direction an electron is spinning in a magnetic field (up or down) Only two electrons per orbital m s = + 1/2 or - 1/2

Letter Analogy Miss Smith 4 The Parkway Kanata ON n= 3 ℓ = 1 m ℓ = -1 m s = +1/2

Quantum Numbers Summary Chart NameSymbolAllowed ValuesProperty Principaln positive integers 1,2,3… Orbital size and energy level Secondaryℓ Integers from 0 to (n-1) Orbital shape (sublevels/subshells) Magneticmℓmℓ Integers –ℓ to +ℓOrbital orientation Spinmsms +½ or –½ Electron spin Direction

Practice! Read p Quantum number handout p. 182 #3-5 p. 184 #3-7