Quantum Mechanical Model of 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

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

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

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