Chem - mystery What has more energy, a heat lamp or a tanning lamp?

The Current 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…

Quantum Mechanics Uses mathematical equations to describe the wave properties of subatomic particles It’s impossible to know the exact position, speed and direction 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

Wave Particle Duality Experimentally, DeBroglie found that light had both wave and particle properties Therefore DeBroglie assumed that any particle (including electrons) traveled in waves Wavelengths must be quantized or they would cancel out

Heisenberg’s Uncertainty Principle Due to the wave and particle nature of matter, it is impossible to precisely predict the position and momentum of an electron Schr Ö dinger’s equation can be used to determine a region of probability for finding an electron (orbital) Substitute in a series of quantum numbers to solve the wave function

Schroedinger's Equation A description of each variable: h - Planck's Constant - Usually (h/2π) is called hbar, and has a value of *10-15 eV·sPlanck's ConstanthbareVs m -mass of the particle being examined.massparticle Ψ - The wave function. This is what is usually being computed using Schroedinger's Equation.wave function V - This is the potential energy of the described particle.potential energy j - The imaginary number, being equal to √-1.imaginary number x - PositionPosition t - TimeTime

Schroedinger’s Cat What’s up with the cat?

Defining the orbital Schroedinger’s calculations suggest the maximum probability of finding an e - in a given region of space with a particular quantity of energy (orbital) Different orbitals are present in atoms having different sizes, shapes and properties There are 4 parameters (called quantum numbers) that define the characteristics of these orbitals and the electrons within them This information provides the basis for our understanding of bonding

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

Quantum Numbers Since an orbital is a 3-D space, we need at least 3 variables to define it, though there are 4 quantum numbers Each electron has a unique set of numbers just as each point on a two- dimensional graph has a unique set of two numbers (x, y).

All four quantum numbers are needed for a complete description of each electron in an atom. The allowed values of the four quantum numbers are restricted and interdependent, indicating the influence of quantization. Can only be certain numbers next number depends on the first

The Pauli Exclusion Principle no two electrons in an atom can have the same set of four quantum numbers, a complete set of four quantum numbers is a unique description of a single electron in a multielectron atom. “the address of the electron”

1. Principal Quantum Number (n) the integer that Bohr used to label the orbits and energy levels of an atom Tells us the size of the orbital n= 1, 2, 3…..∞, n € R The larger n is, the greater the average distance from the nucleus (less stable) The energy gap between successive levels gets smaller as n gets larger The greatest number of electrons possible in each energy level is 2n 2

Distance between energy levels decreases as n increases

2. Angular momentum quantum number ( l ) Is a sublevel of n that tells the shape of the orbital The values of l depend on n For any given n, l = 0 to n-1 The values of l are designated by the letters s, p, d, f, g, h The number of sublevels is equal to the value of n –If n=1, l = 0 s –If n=2, l = 0, 1s, p –If n=3, l = 0, 1, 2s, p, d

Shape of orbitals l 0123 Name of orbital spdf ShapeSphere (1 lobe) 2 lobes4 lobes8 lobes

Shapes of s, p, and d-Orbitals Shapes of orbitals video

d-orbitals Zumdahl, Zumdahl, DeCoste, World of Chemistry  2002, page 336

Shape of f orbitals

3. Magnetic quantum number (m l ) This number indicates the orientation of the orbital in 3-D space m has values related to l, m l = - l, 0, + l –If n = 1, l = 0, m l = 0 –If n = 2, l = 0, 1, m l = -1, 0, +1 (this indicates that there are 3 orbits that have the same energy and shape, but differ only in their orientation in space) –Maximum number of orientations is n 2

Principal Energy Levels 1 and 2 Quantum numbers video

The First Three Quantum Numbers

4. Spin quantum number (m s ) The rotation of the electron in the orbital is either clockwise or counterclockwise m s can have values of + ½ or – ½ Qualitatively we refer to the spin as either clockwise or counterclockwise or up or down

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

Four numbers are required to describe the energy of an electron in an atom

Practice Pg 159 # 3-9, 11