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Quantum Atom

Louis deBroglie Suggested if energy has particle nature then particles should have a wave nature Particle 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 5.97x10 6 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 electron Wave function (Ψ 2 ) – series of solutions that describes the allowed energy levels for electrons Shows regions of probability of finding an electron Regions of high electron density have large values of Ψ 2

Quantum Numbers Orbital – allowed energy state for an electron Principal Quantum Number (n) – same as the Bohr energy level Also called shells Range from n=1 to n=7

Azimuthal Number (l) Called subshells The 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 (m l ) These are the orbitals (hold 2 e - each) Range from – l to + l s m l = 0 ( 1 orbital) p m l = -1, 0, + 1 ( 3 orbitals) d m l = -2, -1, 0, +1, +2 (5 orbitals) f m l = -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?

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