Quantum Atom

Louis deBroglie

Suggested if energy has particle nature then particles should have a wave natureParticle wavelength given by

λ = h/ mv

mv is momentum (mass x velocity)Called matter waves

Matter Wave

Wavelengths of ordinary sized objects are too small to notice

In smaller particles (like electrons) the wavelength becomes significant

What is the λ of an electron with a velocity of 5.97x106 m/s and a mass of 9.11x10-28 kg?

Electron Location

If a subatomic particle exhibits wave properties, we cannot know precisely where its location is

The wave nature of the electron extends it out in space

Uncertainty Principle

Werner Heisenberg suggested that we cannot simultaneously know both the location and momentum of an electron

Pointless to talk about the position of an electron

Quantum Mechanics

Describes mathematically the properties of an electronWave function (Ψ2) – series of solutions that describes the allowed energy levels for electronsShows regions of probability of finding an electronRegions of high electron density have large values of Ψ2

Quantum Numbers

Orbital – allowed energy state for an electron

Principal Quantum Number (n) – same as the Bohr energy levelAlso called shellsRange from n=1 to n=7

Azimuthal Number (l) Called subshellsThe maximum value of l is one less than n l=0 s subshell (spherical) l=1 p subshell (dumbbell) l=2 d subshell (four lobes) l=3 f subshell

Magnetic Quantum Number (ml )These are the orbitals (hold 2 e- each)Range from – l to + l s ml = 0 ( 1 orbital)

p ml = -1, 0, + 1 ( 3 orbitals)

d ml = -2, -1, 0, +1, +2 (5 orbitals)

f ml = -3, -2, -1, 0, +1, +2, +3 (7 orbitals)

Example

Predict the number of subshells in the fourth shell. Give the label of each subshell. How many orbitals are in each?