Electron Configurations and Orbital Diagrams
Locations of Electrons in an Atom.
In quantum theory, each electron in an atom is assigned a set of 4 quantum numbers. Three of these numbers, labeled
n, l, and ml , specify the form of the wave function that give the probability of finding the electron at various points in
space. (Remember that we need three coordinates to specify an object in space.) The fourth quantum number, ms ,is
related to the magnetic spin properties of an atom. The space which is defined by a wave function is termed an Atomic
Orbital. An atomic orbital is a region of space where there is a high probability of finding an electron.
Principal Quantum Number, n
This quantum number determines the energy of an electron. A smaller value of "n" translates to lower energy of the
electron. The size of an orbital also depends on "n". We shall see in a moment that groups (Shells) of several electrons
can have the same number for "n". We use the following notation for shells:
Shell Designation
Letter
(case sensitive)
n
(Principal quantum
number)
K
L
M
N
1
2
3
4
Angular Momentum Quantum Number, l
For a given value of "n", this quantum number represents orbitals of different shapes. It can have any integer value from
0 to n-1. Thus, within a shell of quantum number "n", there are "n" different kinds of orbitals, each with a distinctive
shape denoted by an "l" quantum number. For example, for n=3, the 3 possible values for "l" are 0,1,2, giving rise to
three different shaped orbitals. Orbitals of the same "n", but different "l" are said to belong to different subshells.
Subshell
Letter
l
Subshell Number
s
p
Subshells
d
0
1
2
f
g
3
4
Magnetic Quantum Number, ml
This quantum number distinguishes orbitals of given "n" and "l" (given energy and shape) but have a different orientation
in space. The allowed values are from -1 to +1. For l = 0 (the s subshell) the allowed m1 number is 0 only. Thus there
is only one orbital for the S subshell. For l=1 (the p subshell), ml = -1, 0, +1. There are thus three p orbitals with
different orientations in space.
Spin Quantum Number, ms
An electron acts as if it was a magnet, spinning on it's axis, as the Earth does. The spin quantum number, ms , refers to
two possible orientations of the spin axis, +1/2, -1/2.
Build up of the Atomic Orbitals
We see that quantum mechanics gives a more refined picture of the electrons that surround a nucleus. The atomic
orbitals define a region of space in which there is a high probability of finding electrons. The various shells get
progressively further away from the nucleus.
Shapes of Atomic Orbitals
Atomic orbitals have the following characteristic shapes INDEPENDENT of the value of the n or the main shell:
1. s orbitals have a spherical shape.
Z
Y
X
2. p orbitals have a dumbbell shape. There are 3 p orbitals oriented at right angles, along the x, y and z
axis.
Z
Z
Y
X
Y
Z
X
Y
X
3. d orbitals have a dual dumbbell shape. There are 5 d orbitals are oriented at different angles.
Z
Y
Z
Z
X
Y
X
X
Z
Z
Y
Y
X
Y
X
These diagrams are a mapping of the space which shows the area with the highest probability of locating an electron
around the atom. The atoms float around the atom and have the highest probability of residing in the spaces shown
above.
On the right is a picture of the mathematical probability of finding an
electron around the Carbon atom. Its 1s and 2s orbitals are filled with
two electrons each and two of its 2p orbitals contain one electron each.
The inside orbital is the 1s orbital. The next one out is the 2s orbital.
Then there are the p orbitals surrounding it. The orbital only exists if
there is an electron in it. Since we do not precisely know the location of
the electron, we draw in all three pairs, even though, at only one instance Y
of time, only one pair exists. Each orbital can hold a maximum of 2
electrons. The electrons are spread out equally among the orbitals before
they move onto the next orbital.
Z
X
The table below summarizes the possible sublevels and orbitals that can be found in each principal energy level. Also
note that the maximum numbers of electrons in orbitals, sublevels and principal energy levels can be calculated from
expressions involving quantum numbers.
Principal Energy
Level
Sublevels available
Number of orbitals
in sublevel
(n)
(l)
(2l+1)
1
2
3
4
5
6
s
s
p
s
p
d
s
p
d
f
s
p
d
f
g
s
p
d
f
g
h
1
1
3
1
3
5
1
3
5
7
1
3
5
7
9
1
3
5
7
9
11
Number of
electrons possible
in sublevel
[2(2l+1)]
2
2
6
2
6
10
2
6
10
14
2
6
10
14
18
2
6
10
14
18
22
Total Electrons
possible for energy
level
(2n2)
2
8
18
32
50
72
Orbital diagrams and electron configurations.
Orbital diagrams are used to show how electrons are distributed within sublevels and to show the direction of spin. In
an orbital diagram, each orbital is represented by a box, and each electron is represented by an arrow. The direction of
spin is represented by the direction of the arrow. The orbital diagram for hydrogen, which contains one electron, would
be represented as follows:
1s
An electron configuration is an abbreviated form of the orbital diagram. The electron configuration for hydrogen would
be 1s1. The coefficient 1 indicates that the sole electron occupies the first energy level, and the superscript 1 indicates
that one electron occupies the s orbital within that first energy level.
How do you write the orbital diagram and electron configuration for boron? The atomic number of boron is 5. It has 5
electrons; this means there are electrons in the first and second energy levels. There are two electrons in the first (n=1)
principal energy level, both in an s orbital. There are three electrons in the second principal energy level, two in an s
orbital and one in a p orbital. The electron configuration for boron can be written 1s22s22p1. The orbital diagram can
be written as follows:
2p
1s
2s
Neon, with 10 electrons, could be represented with the electron configuration 1s22s22p6 or with the following orbital
diagram:
2p
1s
2s
Notice that electrons are arranged in accordance with Hund's rule, which states that orbitals of equal energy are each
occupied by one electron before any pairing occurs by adding a second electron. In this way, repulsion between
electrons in a single orbital is minimized, helping to maintain the structure of the atom. All electrons in singly occupied
orbitals must have the same spin. When two electrons occupy an orbital they have opposite spins.
You can write electron configurations yourself as long as you keep in mind the maximum number of electrons allowed in
each orbital and the order in which orbitals are filled. For an atom in the ground state, electrons fill the orbitals beginning
with the lowest energy orbital before filling orbitals with successively higher energies.
The figure below shows a sequence
model that can be used to write
electron configurations. Notice that
principal energy levels do not always fill
in order. You can see in the drawing,
which shows the energy distribution of
orbitals, that there are areas where
principal energy levels overlap. Notice
that even though the 3d orbital is in a
lower principal energy level, it is higher
in energy than the 4s. Therefore a 4s
orbital generally fills before a 3d orbital.
1s
4f
5f
3d
4d
5d
6d
1s
2p
3p
4p
5p
6p
1s
7p
1s
2s
3s
4s
5s
6s
1s
7s
1s
The electron configuration for gallium,
1s22s22p63s23p64s23d104p1, shows why you need to understand the above diagram and the one shown below to write
it's orbital diagram.
4p
3d
4s
3p
2p
1s
3s
2s
Energy generally increases as n, the principal
energy level, increases. It is possible, however
for the lowest sublevel of n=4 to be below the
highest sublevel of n=3. This occurs in
potassium and calcium atoms, where successive
electrons enter the 4s rather than the 3d sublevel.
How to Write an Electron Configuration:
4f
4d
4
E
3
1. Locate the element whose electron
configuration you wish to write in the
periodic table. For example, locate oxygen.
Use the atomic number to determine the number
of electrons in one atom. Oxygen has eight
electrons.
4p
3d
4s
3p
3s
2p
2
2s
1
1s
2. Fill orbitals in the proper order with
electrons . Keep in mind which sublevels and orbitals are found in each energy level. Keep filing orbitals using the
order shown in the figure above (with the spheres) until you have placed all the electrons of the element whose
configuration you are writing. The electron configuration for oxygen is as follows:
1s22s22p4
3. Check that the total number of electrons in the electron configuration equals the atomic number. For
oxygen, the total number of electrons shown in the electron configuration is 2+2+4 or 8. This is equal to the atomic
number of oxygen.
Electron configurations can be written in terms of noble gases.
Electron configurations can be abbreviated to save space. For example, the electron configuration for sodium, Na,
could be written as 1s22s22p63s1. However, to shorten this, we could also write:
[Ne]3s1
The sodium block is the first one in the table that shows filling of the 3s orbital. The preceding noble gas, neon, ends the
row in the previous period by completely filling the 2p orbital. You can use the symbol for neon to represent all the
filled orbitals through 2p.
Problems:
1. Write the electron configurations for phosphorus and nickel. Then draw the orbital diagrams for these elements.
2. Write the complete electron configurations for magnesium, sulfur, and potassium. Then write their electron
configurations using the symbols for the noble gases.
3. What element is represented by [Ne]3s23p6?
4. Determine the electron configuration for the last electron of the following elements: S, Pt, Sr, K, and Al.
5. The an unknown element has an electron configuration of 1s22s22p63s23p4.
A. What is the element?
B. What does the superscript 6 refer to?
C. What does the letter s refer to?
D. What does the coefficient 3 refer to?
6. Write the electron configuration for calcium, a nutrient essential to healthy bone growth and development.
7. Write the electron configuration for copper, which is used in pennies.
8. Use the symbols for the noble gases to write the electron configurations for the following elements:
A. Zr
B. U
C. Rn
9. Write the electron configuration and draw the orbital diagrams for the following elements:
A. Carbon
B. Silver
C. Aluminum
10. Write the electron configuration and draw the orbital diagrams for the following elements:
A. Ti
B. Rb
C. Na