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Orbitals
Because of observations made regarding ionization energy, the fine structure of element spectra, and new
discoveries made regarding the wave nature of matter (specifically, electrons), scientists came up with a
new model of the atom. In order to write a mathematical expression that would allow them to predict
ionization energies and calculate the wavelengths that show up in an element’s spectrum (which is precisely
what Niels Bohr was trying to do, but only managed to do it for Hydrogen), it was necessary to take into
consideration more than just what energy level a particular electron is in. Scientists deduced that there
must be 4 “properties” of electrons and these 4 properties are called quantum numbers. Every electron can
be completely described with its 4 quantum numbers and no two electrons within the same atom have the
same 4 quantum numbers. Given the four quantum numbers, the mathematical equations can be solved for
each electron to give ionization energies or other spectroscopic data.
The 4 quantum numbers are:
o
n or principle quantum number
o
l or orbital quantum number
o
ml or magnetic quantum number
o
ms or spin quantum number
Symbol
Name
Spectroscopy
Possible
Values
Classical
Meaning
Actual
Meaning
n
principle
the sharpest line
1, 2, 3, …
Orbit
Energy
level
l
orbital
The more detailed structure of the
spectrum that kind of blur t give n.
Not observed until tools got better
0, 1, 2, …(n-1)
Shape of
orbit
Sublevel,
(s,p,d,f)
ml
magnetic
Observed when the element spectrum
is observed in a magnetic field
-(l-1)…(l+1)
3-d shape
of orbit
Orbital (on
s orbital, 3
p orbitals)
ms
spin
Needed to make the equations work out
+1/2 or – 1/2
Direction
of electron
movement
Magnetic
moment of
electron
Exercise 1
(a) Give all the possible orbital quantum numbers for energy level 1, 2, 3
(b) Give all the possible magnetic quantum numbers for energy level 2
The difference between the classical meaning and the actual meaning of the quantum numbers is that in the
classical meaning, scientists still thought of electrons as particles orbiting a nucleus in a defined path. Once
Schroedinger showed that treating an electron as a wave resulted in calculations that accurately predicted
properties of the elements, we couldn’t really think of electrons as travelling in defined paths. In addition,
Heisenberg stated that there is a limitation to what we are actually able to measure. There is a theoretical
limit to how small the uncertainty in our measurements can be. Therefore, we can never know both the
position and the speed of an electron. If we have measured it’s position very precisely than by doing that
we must have affected its speed and, therefore, don’t have any idea how fast it’s travelling. So…we can’t
know where its going to be at any time in the future. If we measure it’s speed than we must have affected
its position and if we don’t know where it was to begin with, than knowing its speed doesn’t help us predict
where it is at a later time. So…we can only say where an electron is LIKELY to be and that is what an
orbital is: a 3-Dimensional space predicting, with a 98% probability of where an electron could be.
As a help in picturing the orbitals imagine you were able to take a large number of photographs of a
hydrogen atom, containing one electron. By superimposing these photographs, you would get an impression of
where the electron spends most of its time. The picture you would get would be something like the one
below.
The picture is itself an over-simplification since it is restricted to two dimensions. The complete model is
three-dimensional and spherical. Since even the two-dimensional picture is tedious to draw, we often use
instead a boundary round the region where the probability of finding an electron is high - about 98% - as
shown below.
Each energy level has between 1 and 4 sublevels and each sublevel is associated with a particularly shaped
probability density.
Exercise 2
Associate the pictures below with the quantum numbers.
The shape of s, p and d orbitals
Note :

The orbitals are 3-dimensional and not precisely defined. The charge density falls off sharply at a
certain distance from the nucleus.

All s-orbitals are spherical 1s < 2s < 3s etc.

All p-orbitals are dumbell shaped in 3 directions in space 2p < 3p < 4p.
Exercise 3
Observe the grand orbital table at: http://www.orbitals.com/orb/orbtable.htm
And the orbital movies (my website under atomic structure resources). Record your observations.
Exercise 4
Each orbital can only hold 2 electrons. Explain why this must be true given the Pauli Exclusion Principle that
no two electrons can have the same four quantum numbers.
Exercise 5
(a) Observe the patterns and make predictions for energy level 5
(b) Fill in the blanks with the appropriate quantum number
Quantum shell
Sub-shells
n=1
One sub-shell
K shell
Number of
electrons
1
1s sub-shell
n=2
n =3
n=4
n=5
L shell
M shell
N shell
Number of orbitals
2
Two sub-shells
2s sub-shell
___
2
8
1
2p sub-shell
___
6
3
1
Three sub-shells
3s sub-shell
___
2
3p sub-shell
___
6
3d sub-shell
___
10
5
4s sub-shell
___
2
1
4p sub-shell
___
6
4d sub-shell
___
10
5
4f sub-shell
___
14
7
Predict…
Predict…
18
3
Four sub-shells
Predict…
32
3
Now that you know what an orbital is, you need to know how to use the orbital to describe the electron
structure of elements. There are two ways to do this:
(1) electron configurations
a.
Standard: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 …
b. More detailed: 1s2 2s2 2px2 2py2 2pz2 3s2 3px2 3py2 3pz2 4s2 3dz22 3dx2-y22 3dxy2 3dxz2 3dyz2…
i. Since all p orbitals are degenerate (have the same energy) it doesn’t matter which
one you put electrons in first, but see below for Hund’s rule
ii. Same goes for d orbitals and f orbitals
c.
Noble Gas: [Ne] 3s2 …
(2) orbital diagrams (arrows)
Aufbau described the order that electrons fill the orbitals: from lowest to highest energy. It may seem a
little odd, but the 4s orbital is actually lower in energy than the d orbitals in the 3 rd energy level. To
remember the order you can use the following :
In an atom the orbitals are filled in order of increasing energy, starting from 1s.
An aid to remembering the order in which orbitals are filled is to write them down in columns as shown.
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
The order of filling is then given by drawing diagonal lines through the symbols.
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
Exercise 6
Write out the complete order in which orbitals are filled:
One other rule you must know: Hund’s Rule
Degenerate orbitals (of the same energy) are occupied by one electron before any orbital is occupied by a
second electron and all electrons in singly occupied orbitals must have the same spin.
Exercise 7
On a separate sheet of paper write the electron configuration and orbital diagrams for elements 3 to 10.
Exercise 8
Give the quantum numbers for all 8 of oxygen’s electrons.
Exercise 9
An electron has quantum numbers( n, l, ml, ms): 3, 0, 0, +1/2
(a) In what energy level is the electron located?
(b) In what subshell is the electron located?
(c) What is the shape of this subshell?
An electron has quantum numbers: 3, 1, -1, -1/2, draw it’s orbital diagram.
Exercise 8
(a) Write the electron configuration for Na.
(b) Explain why the electron configuration for Na can be written [Ne] 3s 1
Exercise 9
(a) Relate electron configuration and location on the periodic table.
(b) What group has electron configurations that end in s1?
(c) What group has electron configurations that end in p2?
(d) What group has electron configuration that end in d 3?
Exercise 10
(a) According to our IE graphs, boron and aluminium had a lower IE than expected. Why?
(b) According to our IE graphs, oxygen and sulphur had a lower IE than expected. Why?
Exercise 11
(a) Write the electron configuration for Copper and Chromium.
(b) According to that awesome fancy periodic table I gave you at the beginning of the year, what is the
electron configuration for copper and chromium?
(c) Why do you think the actual e-config is different than predicted? (Hint: everything in chemistry has
to do with energy)