Transcript The Quantum Mechanical Model of the Atom

The Quantum Mechanical
Model of the Atom
= model in which e- are treated as
having wave characteristics
With Bohr’s model, so far we’ve
been able to explain
Atomic line spectra
 Energy states within the atom

Still haven’t explained:
 What the e- is doing inside the atom
 Where the e- spend their time
 Complex line spectra of multi-e- atoms
Wave-particle duality of Electrons
Light has been regarded as having waveparticle duality.
 Waves: a continuous traveling
disturbance
 Particles: discrete bundles


Distinctions appear to break down on the
atomic level.
Louie de Broglie & Matter Waves 1923

h

m

If waves behave like
particles, then particles
should be able to behave like
waves.
The wavelength for particles
should be:
Where
h = Planck’s constant,
m = the mass of the particle
υ = the speed of the particle

Applying De Broglie equation:
Calculate the wavelength of a 60-kg sprinter
running at 10 m/s.
Too small to be
detected
The wave character of e- led to
useful application of electron
microscope in 1933
Dust mites
Erwin Schrödinger - Wave equation (1926)
A wave theory and equations required
to fully explain matter waves.
Called psi
An equation with 2 unknowns:
E = allowed energy level of atom
𝞇 = wavefunction; a mathematical description of the
electron
H= the “hamiltonian”; not a variable,
a set of mathematical instructions to be performed on 𝞇
Schrödinger equation
Looks
like
Fun!!!
•
•
Only certain Energy values will result in
answers (wavefunctions), 𝞇
Plotting |𝞇2| enables us to “see” the electron
orbital
An atomic orbital can be visualized as
a fuzzy cloud where the electron is
most likely to be at a given energy
level
Orbitals:
𝞇2 for E 1 (n=1) plotted in 3-D
 Both are orbitals 
probability density
probability surface
(≥95% probability)
A few notes:
• 𝞇2 is large near the nucleus  meaning e- most
likely found in this region
• Value of 𝞇2 decreases as distance form nucleus
increases, but 𝞇2 never goes to zero  probability
of finding e- far from nucleus is small
• Also means an atom doesn’t have a definite
boundary, unlike the Bohr model
Heisenberg’s
Uncertainty Principle - 1927
Werner Heisenberg
It is impossible to determine
simultaneously the exact position
and momentum of a single atomic
particle
x mv > h/4
Uncertainty in
position
Uncertainty
in momentum
Planck’s constant
(6.626 x 10-34 J s )
We cannot know the exact position of the electron;
only where the electron is most likely to be.
Quantum Numbers:
A set of 4 quantum numbers give
information about each orbital and each
electron
n,
l, ml , ms
Tell us the characteristics of the
electron waveforms
So, this picture we’ve learnt from
grade 9 is no longer correct
The most recent, accepted
model of an atom looks like this
Watch Quantum mechanic
short clip
A beautiful amalgamation of
the quantum mechanical model
of atom