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de Broglie, the Uncertainty Principle, and Quantum
Mechanics
THE WAVE NATURE OF MATTER
Dual Nature of Matter?!
• By the early 1920s, the theory of the waveparticle duality of light had been accepted
• But in 1923, a young scientist by the name of
Louis de Broglie was ready to shock the scientific
community with another hypothesis:
• Matter can exhibit wave-like properties!
de Broglie and the Wave Nature of
Matter
• de Broglie proposed that a particle with mass, m, moving at a
speed, v, other than the speed of light will have a wave nature
consistent with a wavelength given by the equation:
h
λ=
mν
λ
=
wavelength, meters
h
=
Planck’s constant
m
=
mass, kg
v
=
velocity, m/s
• This equation shows that large objects have wavelengths too short
to observe, but small objects (like electrons) have longer and more
readily observable wavelengths
Incorporating the Wave Nature of
Matter in the Atomic Model
• Current ideas about atomic structure are based on De
Broglie’s theory
• The treatment of atomic structure using the wave-like
properties of the electron is called quantum mechanics
(or wave mechanics)
• In contrast to Bohr’s precise atomic orbits, quantum
mechanics provides a “less certain” picture of the
hydrogen atom
• Enter Erwin Schrӧdinger…
Erwin Schrödinger and the
Quantum Model of the Atom
• In 1926, Erwin Schrödinger used de Broglie’s theory to develop an
equation (Schrödinger’s wave equation) describing the locations
& energies of the electron in a hydrogen atom
h2
−
8π2 m
• General equation:
d2 Ψ
dx 2
+ VΨ = EΨ
ĤΨ = EΨ
• Acceptable solutions to Schrödinger’s wave equation are called
wave functions ()
• Unlike Bohr’s model, these wave functions do not describe the
exact location of an electron
An Overview of the Quantum
Mechanical Model
• The square of a wave function (2) gives the probability of
finding an electron in a particular infinitesimally small volume
of space in an atom
• Because we are treating electrons as waves (not particles), we
cannot pinpoint the specific location of an electron!
• Instead, mathematical solutions to the wave functions give 3dimensional shapes (orbitals) within which electrons can
usually be found
What do Electron Orbitals Look Like?
• These 3-D orbitals (probability clouds) take the place of Bohr’s
simple well-defined orbits in the modern model of the atom
• We don’t know exactly where the electrons are!
• This “less certain” model is justified by an important principle of
science established in 1927 called the Heisenberg Uncertainty
Principle
So, What Does the Principle State?
“It is impossible to determine the exact location and the exact
momentum of a tiny particle like an electron”
• The very act of measurement would affect the position and
momentum of the electron because of its very small size and
mass
• The collision of an electron with a high-energy photon (required to
locate the electron) would change the momentum of the electron
• The collision of an electron with a low-energy photon would not
provide much information about the location of the electron
A Macroscale Analogy of the Heisenberg
Uncertainty Principle
High Shutter Speed
Low Shutter Speed
Can judge location,
but not speed
Can judge speed,
but not location
But…
• I still don’t understand what an orbital is!
Time for “Locating an Electron in an Atom by
Analogy” activity!
• Be sure the peas are dropped from a consistent height
• You must mark each landing spot with an “X” using a pencil!
• Before you begin:
• Do you expect each group to get the same pattern?
• Do you expect a pea to land exactly in the middle?