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Electrons as waves
• Scientists accepted the fact that light has a
dual wave- particle nature.
• De Broglie pointed out that in many ways
the behavior of the Bohr’s quantized
electron orbits was similar to the known
behavior of waves.
• Electrons should be thought of as having a
dual wave-particle nature also.
Evidence; Electrons
• Electron beams could be diffracted or bent.
• Electron beams demonstrated the properties
of interference.
Heisenberg Uncertainty Principle
• Werner Heisenberg (1927)
• It is impossible to determine simultaneously
both the position, and velocity, of an
electron or any other particle.
Heisenberg explained
• To locate an object you would have to be
able to look at it.
• When we see an object we actually are
seeing the light waves that the object
• For us to see an object a photon of light has
to hit it.
Heisenberg explained
• A photon hitting a book or an airplane has
no noticeable affect.
• However, an electron is so small that once a
photon its it, the electron undergoes a large
energy change and is moved.
• Similarly, the collision between the photon
and the electron causes the electrons
velocity to change.
In summary
• If we were able to measure the location, the
velocity would change
• If we were to measure the velocity, the
location will change.
• Note: Treats electron like a particle
Schrodinger ‘s wave equation
• Developed an equation that treats electrons
as waves. ( related the amplitude of the
electron wave to any point in space around
the nucleus).
Quantum theory
• Heisenberg’s uncertainty principle and
Schrodinger’s equation laid the foundation
for quantum theory.
• Quantum theory- describes mathematically
the wave properties of electrons and other
very small particles.
• Ceiling fan- where are the blades at any one
• Three dimensional region around the nucleus that
indicates the probable location of an electron.
• These three dimensional shapes are named s, p, d,
and f.
• When describing the location of the electrons in
an orbital we are indicating that there is a 99 %
chance that the electron will be found there.
Quantum numbers
• A list of three numbers that describe the
location of the electron
• The numbers represent
– The main energy level
– The shape
– The orientation of the orbital, axis
Spin of electron
• A fourth number indicates the spin within
the orbital.
Principle quantum number
• 1-7 representing the energy level
• Symbolized by the letter n
• As n increases the distance from the nucleus
• As n increases the potential energy of the
electron increases.
Angular momentum or orbitals
• The different shaped orbitals are also called
• Symbolized by l, indicates the shape of the
• 2 electrons are allowed in one orbital
• The number of orbital shapes, l, possible is
equal to n ( up to n=4)
• The values of l allowed are 0 and all
possible integers up to n-1
• l= n-1
0 = s shape
1 = p shape
2 = d shape
3 = f shape
2 electrons per orbital
The s shape has 1 orbital – total of 2 electrons
The p shape has 3 orbitals – 6 electrons
The d shape has 5 orbitals – 10 electrons
The f shape has 7 orbitals – 14 electrons
• See page 103
• Each orbital is on a different axis, ( x,y,z etc. )
Magnetic quantum number
• Indicates the orientation of the orbital
around the nucleus.
• Symbolized by the letter m
• Indicated by numbers on either side of zero
• The s shape has an m value of 0 ( no axis)
• The p shape has m values of –1,0,+1
• The d shape has m values of –2,-1,0,+1,+2
• n,l,m
• Energy level, shape, axis
The last number is a spin indicator
• -1/2 or + ½
• These are the two spin states, ( spin to the right or
spin to the left)
• No two electrons can be identical., or , no two
electrons can have the same set of quantum
numbers – Pauli’s exclusion principle
• A maximum of two electrons can occupy an
orbital, each will have a different spin.
Mathematical equations
• The number of orbitals per energy level is
n=2, there are 4 orbitals; 1 s and 3 p
n=3 there are 9 orbitals; 1s, 3p, 5d
Number of electrons
• Since there are 2 electrons per orbital
• 2n2 is the number of electrons per energy