Chem 150
Week 10
Handout 2
Orbitals of the Hydrogen Atom
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Orbitals are wave functions
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The square of the wave function, Y2 gives the three-dimensional probability distribution.
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We commonly draw orbitals as these probability distributions.
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Orbitals have nodes and exhibit phase behavior just like other waves.
s Orbitals
Value of l = 0.
Spherical in shape.
Radius of sphere increases with increasing value of n.
Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that
s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.
Remember the shape, orientation and phases of the s and p orbitals. You must be able to draw these!!!
The three p Orbitals
Fig. 8-28, pg 311
Consider the following orbitals:
3py
3dx2-y2
2pz
4s
4px
Which has the most nodal planes (angular nodes)?
Which has the most radial nodes?
Which has the least electron density in the xy plane?
Which is degenerate with the greatest number of other orbitals?
Which has the greatest value of l?
Electron Configurations
Electron configuration is used to show how electrons are distributed among orbitals.
4 RULES FOR ASSIGNING ELECTRONS TO ORBITALS
1. Electrons occupy orbitals in a way that minimizes the energy of the atom.
This has been established by experiment:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
2. No two electrons in an atom may have the same four quantum numbers.
This is called the Pauli exclusion principle. Only two electrons may occupy the same orbital, and
these two electrons must have opposing spins. The electron capacity of a subshell = 4l + 2
3. Hund’s rule: when orbitals of identical energy (degenerate) are available, electrons occupy
these orbitals singly when possible.
Since electrons are charged, they prefer to stay far apart.
Atoms have as many unpaired electrons as possible.
4. Electrons in different singly occupied orbitals of the same subshell have the same or parallel
spins.
In carbon for the 2p subshell: Electron configuration for carbon: 1s22s22p2
1s
2s
2p
NOT
1s
2s
2p
The Aufbau Process: Electron configurations of the elements are assigned by “building up” and
describing the orbital the added electron goes into.
Z = 1,
Z = 2,
Z = 3,
Z = 4,
Z = 5,
Z = 6,
Z = 7,
Z = 8,
Z = 9,
Z = 10,
1s1
1s2
1s22s1
1s22s2
1s22s22p1
1s22s22p2
1s22s22p3
1s22s22p4
1s22s22p5
1s22s22p6
H
He
Li
Be
B
C
N
O
F
Ne
For Z = 11-18 (Na through Ar)
All these elements have the 1s, 2s, 2p subshells filled (1s22s22p6). This is the Ne configuration,
so for Na-Ar we abbreviate the core [Ne]
[Ne]3s1
[Ne]3s2
…
[Ne]3s23p6
Z = 11, Na
Z = 12, Mg
…
Z = 18, Ar
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Electrons in the outermost electron shell are called valence electrons.
ie, for Ar: [Ne]3s23p6, the 3s23p6 electrons are valence electrons.
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Z = 19 and 20 (K and Ca), fill the 4s subshell
K: [Ar]4s1
and
Ca: [Ar]4s2
Z = 21-30, Sc to Zn, fill the 3d subshell
can write Sc: [Ar]3d14s2 or
[Ar]4s23d1
both are correct.
Two exceptions to regular filling of 3d orbitals: Cr has [Ar]4s1 3d5 and Cu has [Ar]4s1 3d10
because it lowers the energy of the whole atom to have a half filled or filled d-subshell.
V
Ni
4s
3d
Cr
4s
3d
4s
3d
Cu
4s
3d
Fig. 8-38
Pg. 322
Source: Petrucci
Paramagnetism and diamagnetism: A spinning electron induces a magnetic field
When all electrons are paired, the individual magnetic effects cancel out, the species is
diamagnetic. With one or more unpaired electrons, the individual magnetic effects do not
cancel out and the species is paramagnetic. It is attracted to a magnetic field. In some cases, the
magnetic properties are temporary while in other the magnetic field is permanent.
Note that the magnetic properties of gas phase atoms do not necessarily represent those of bulk
phase matter!
Materials with magnetic properties have many applications in our life: electro motors,
generators, transformers computer data storage, audio/ video data recording (hard drive disk,
floppy disk) high-speed read/write heads in disk memory devices, magnetic stripes on credit
cards, bank card, dipole magnets for beam handling in particle accelerators, loudspeaker,
sensor.