Download Unit 3 Reading 2

Tony Manly – Poway High School
Shells, Subshells and Orbitals Handout
“the addresses of electrons”
There are 4 Quantum numbers to describe the location of an electron in an atom.
Symbolically these four aspects of describing where electrons are found in atoms are
represented by letters: n, l, m, s. The first three quantum numbers are calculated from the
Schrödinger equation.
Any question in an atom can be described by its own unique set of these 4 quantum numbers.
1. The First Quantum Number (n)
[Energy levels or Shells]
√
Each electron has its own frequency, so it has its own energy, so it occupies a specific
energy location in the atom. We say that an electron is quantized. The first major energy
description or location is called the energy level or shell.
√
Energy levels range in value from one to infinity. In nature, the known elements have energy
level or n-values from 1 to 7. The larger the value of n, the greater the average distance the
electron is from nucleus in the atom.
√
An electron of any atom can be found in any higher energy level of that atom (if energy is
added to move it to a higher energy level).
√
The greatest number of electrons in an energy level = 2 n2.
2(4)2 = 32
n=4
E
n
e
r
g
y
2(2)2 = 8
n=2
n=1
√
2(3)2 = 18
n=3
2(1)2 = 2
Note what happens to the energy difference between energy levels as you get further and
further from the nucleus of the atom. This decreasing energy difference means that outer
energy levels are closer and closer to the previous energy level.
2. The Second Quantum Number (l)
[Sublevels or Subshells]
√
Spectrum studies show that each energy level is actually made of energy subdivisions which
are grouped together to make up the energy level. These are called sublevels or subshells.
√
Each energy level (n) has (n) sublevels.
These sublevels are designated: s, p, d, f, g, h, i
For:
n= 1, sublevel is: s
n= 2, sublevels are: s, p
n= 3, sublevels are: s, p, d
n= 4, sublevels are: s, p, d, f
3. The Third Quantum Number (m)
[Orbitals]
√
Each sublevel (l) is comoposed of one or more orbitals.
√
Individual orbitals are identified by their direction in space using the Cartesian coordinates
(x, Y, Z axes in graphing).
√
The m values (number of orbitals within a sublevel) are integers from -l to +l.
Number of orbitals
For
l=0, orbitals are:
0
1
l=1, orbitals are:
-1
0
+1
3
l=2, orbitals are:
-2
-1
0
+1
+2
5
l=3, orbitals are:
-3
-2
-1
0
+1
+2
+3
7
You can remember that the orbitals follow an “odd progression” of values from one to an infinite
odd number.
4. The Fourth Quantum Number (s)
√
[
]
Any given electron can spin only one of 2 ways: clockwise or counter-clockwise. This is
indicated with an arrow pointing up or down.
An electron tends to occupy the lowest energy location in the atom.
Q: Why then don’t all electrons in an atom occupy the 1s orbital (the lowest energy location)?
A: No more than two electrons can occupy an atomic orbital, and for two electrons to share the
same orbital, they must have opposite spins.
How are electrons distributed into energy levels, sublevels and orbitals?
An electron location in an atom follows these principles or rules:
1. Aufbau Principle
√ Electrons enter orbitals of lowest energy first. See also the Diagonal Rule.
√
Electrons in sublevels of higher energy levels (n) have generally a higher energy?
√
For electrons in orbitals with the same n value, the higher l values are those at higher
energies.
2. Pauli Exclusion Principle – (Wolfgang Pauli)
√ Only two electrons per orbital – one of each spin direction.
3. Hund’s Rule
√ When electrons occupy orbitals of equal energy, one electron enters each orbital until all the
orbitals contain one electron with spin parallel. Then, the paired electrons fill the orbitals to
fill them with 2 electrons each.
No 2 electrons can have
the same set of 4 Quantum Numbers.
Table 1
First
Quantum
Number, n
(energy
level)
Summary of Quantum Numbers
Second
Quantum
Number, l
(sublevel)
0
1
2
Sublevel
Designation
Third Quantum
Number, m
(orbitals)
Number
of
Orbitals
in
Sublevel
Maximum
number of
electrons
1s
0
1
2
2s
2p
0
-1 0 +1
1
3
8
3s
3p
3d
0
-1 0 +1
-2 -1 0 +1 +2
1
3
5
18
4s
4p
4d
4f
0
-1 0 +1
-2 -1 0 +1 +2
-3 -2 -1 0 +1 +2 +3
1
3
5
7
32
0
1
0
1
2
3
0
1
2
3
4
The Diagonal Rule:
The order of filling sublevels.
1s2
2s2
2p6
3s2
3p6
3d10
4s2
4p6
4d10 4f14
5s2
5p6
5d10 5f14 5g18
6s2
6p6
6d10 6f14
7s2
7p6
Table 2
Electron energy level diagram for atomic orbitals.
n
7
5f
7s
6p
5d
4f
6
6s
5p
4d
5
5s
4p
3d
4
4s
3
3s
2
2s
1
1s
E
N
E
R
G
Y
3p
2p