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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 5.97x106 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
electron
Wave function (Ψ2) – 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 Ψ2
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 (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?