ELECTRONS IN ATOMS
Quantum Numbers, Orbitals,
And Electron Configurations
Solving equations
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3x = 15
One solution
X2 = 9
Two solutions
Schrodinger’s Equation
Infinite solutions
Schrodinger’s solutions
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An infinite number
Each is a set of four values
Called “quantum numbers”
n,l,m,s
In a given atom, each electron has a unique
set
• This is that electron’s “address”
The First Quantum Number
• Principal quantum number
n
• Values
 n = 1,2,3,….∞
• What it tells us:
 Orbital energy level
 Orbital size
 Number of nodes (n-1)
The Second Quantum Number
• Angular Momentum quantum number
l
• Values
 l = 0, 1,2,3,… (n-1)
• What it tells us:
 Orbital energy sub-level
 Orbital shape
 Number of non-spherical nodes
Meaning of l values
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l=0
l=1
l=2
l=3
“s orbital”
“p orbital”
“d orbital”
“f orbital”
shape = spherical
shape = dumbbell
shape = double dumbbell
shape is more complex
The Third Quantum Number
• Magnetic quantum number
m
• Values
 m = -l, … -1, 0, +1, …+l
• What it tells us:
 Orbital orientation (direction)
Possible m Values and Meanings
• This slide under construction…
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s orbitals occur singly
p orbitals occur in sets of 3
d orbitals occur in sets of 5
f orbitals occur in sets of 7
The Fourth Quantum Number
• Spin quantum number
s
• Values – only two possible
 s = -1/2 or +1/2
 Usually described as “up spin” or “down spin”
• What it tells us:
 The “spin” of an electron
 This is the only quantum number that describes a
particle aspect of the electron
Probability Distributions
• What is the electron doing in the orbital? We
don't know, and we can't know, and so we just
ignore the problem! All you can say is that if
an electron is in a particular orbital it will have
a particular definable energy.
• http://www.chemguide.co.uk/atoms/properti
es/atomorbs.html (and following slide visuals:)
Probability distributions for s orbitals
Probability distributions for p orbitals
The Credit:
• The link below has excellent visuals of many of
the orbitals. Much of the wording on the
following slides is copied directly from this
(“ORBITRON”) site.
• http://winter.group.shef.ac.uk/orbitron/
1s orbital
• For any atom there is just one 1s orbital.
Consider the shape on the left. The surface of
the shape represents points for which the
electron density for that orbital is the same an isosurface. The image shows clearly the
spherical shape of the 1s function.
• http://winter.group.shef.ac.uk/orbitron/AOs/1
s/index.html
2s orbital
• For any atom there is just one 2s orbital.
• The image on the left is deceptively simple as the
interesting feature is buried within the orbital.
That on the right is sliced in half to show that
there is a spherical node in the 2s orbital.
• While still spherical, the higher s-orbitals (3s, 4s,
5s, 6s, and 7s) are more complex since they have
more spherical nodes.
• http://winter.group.shef.ac.uk/orbitron/AOs/2s/i
ndex.html
2p orbitals -- NOT
• It is common to denote the shapes of 2p
orbitals … as shown below. These "figure-ofeight" style pictures … make the orbitals
appear much "thinner" than they are really,
and also that there are sharp "points" in the
region of the nucleus, which there are not.
2p orbitals
• For any atom, there are three 2p orbitals. These orbitals have the
same shape but are aligned differently in space. The three 2p
orbitals normally used are labelled 2px, 2py, and 2pz since the
functions are "aligned" along the x, y, and z axes respectively.
• Each 2p orbital has two lobes. There is a planar node normal to the
axis of the orbital (so the 2px orbital has a yz nodal plane, for
instance). The higher p-orbitals (3p, 4p, 5p, 6p, and 7p) are more
complex still since they have spherical nodes as well.
• The origin of the planar node becomes clear if we examine the
wave equation which, for instance, includes an x term in the case of
the 2px orbital. Clearly When x = 0, then we must have a node, and
this by definition is the yz plane.
• http://winter.group.shef.ac.uk/orbitron/AOs/2p/index.html
3p, 6p, 7p
• http://winter.group.shef.ac.uk/orbitron/AOs/3
p/index.html
• http://winter.group.shef.ac.uk/orbitron/AOs/6
p/index.html
• http://winter.group.shef.ac.uk/orbitron/AOs/7
p/index.html
3d orbitals
• For each atom, there are five 3d orbitals. These are labelled
3dxy, 3dxz, 3dyz, 3dx2-y2 and 3dz2. Four of these functions
have the same shape but are aligned differently in space.
The fifth function (3dz2) has a different shape.
• Each 3dxy, 3dxz, 3dyz, and 3dx2-y2 orbital has four lobes. There
are two planar node normal to the axis of the orbital (so
the 3dxy orbital has yz and xz nodal planes, for instance).
The 3dz2 orbital is different and has two conical nodes.
• http://winter.group.shef.ac.uk/orbitron/AOs/3d/index.html
• The higher d-orbitals (4d, 5d, and 6d) are
more complex since they have some spherical
nodes.
• http://winter.group.shef.ac.uk/orbitron/AOs/4
d/index.html
• http://winter.group.shef.ac.uk/orbitron/AOs/6
d/index.html
• http://winter.group.shef.ac.uk/orbitron/AOs/7
d/index.html
4f orbitals
• For any atom, there are seven 4f orbitals. The
f-orbitals are unusual in that there are two
sets of orbitals in common use. Those shown
here are the cubic set . … The other set is
known as the general set.
• http://winter.group.shef.ac.uk/orbitron/AOs/4
f/index.html
Orbital Filling Game
• http://www.learner.org/interactives/periodic/
elementary2.html
Another good reference
• http://antoine.frostburg.edu/chem/senese/10
1/electrons/