2.5.3.2. Electron Shells
As a simple model, an atom may be considered to be a positively charged nucleus surrounded by shells of negatively charged electrons. The shells are termed K, L, M, and N (starting from the innermost, most strongly bound shell). More accurately, an atom consists of a nucleus surrounded by electrons that occupy volumes of space (orbitals) around it (Figure 2.5.3.2) only some of which are spherical.
| Figure 2.5.3.2. Actual probability distributions for electron clouds, which are considered as shells in this discussion. |
 |
Each electron has several quantum numbers that uniquely define it and specify the shell it may occupy. The quantum numbers are:
|
Number |
Name |
Permitted Values |
Defines |
Notes |
|
n |
principal quantum number |
positive integers (1,2,3...) |
electron shell (1=K, 2=L, 3= M...) |
Principle binding energy. |
|
l |
azimuthal quantum number |
integers from 0 to (n-1) |
electron cloud shape (0=sphere, 1=dumbbell...) |
Orbital angular momentum. Chemists follow the conventions of optical spectroscopy using letters rather than numbers to indicate the value of l: sharp (l = 0), principal, (l = 1), diffuse (l = 2), and fundamental (l = 3). |
|
m |
magnetic quantum number |
-l to +l (including 0) |
electron shell orientation when in a magnetic field |
In the absence of an external magnetic field, the magnetic number has no meaning and will be ignored in the subsequent discussion. |
|
s |
spin quantum number |
± ½ |
electron spin direction |
Clockwise or counterclockwise. |
|
j |
inner precession |
l ± ½, except j ¹ 0 - ½ |
total angular momentum |
As noted under permitted values, for s orbitals (with l = 0), j can only be +½ (a vector sum is always positive). The value of j is important for determining what transitions are possible between electron shells. |
The Pauli exclusion principle states that no two electrons can have the same quantum numbers. This constraint specifies the maximum number of electrons per level as 2n². Shells specified by the quantum numbers are labeled as shown on the following table.
|
|
K |
LI |
LII |
LIII |
MI |
MII |
MIII |
MIV |
MV |
NI |
NII |
NIII |
NIV |
NV |
NVI |
NVII |
|
n |
1 |
2 |
2 |
2 |
3 |
3 |
3 |
3 |
3 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
|
l |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
2 |
2 |
0 |
1 |
1 |
2 |
2 |
3 |
3 |
|
s |
+½ |
+½ |
-½ |
+½ |
+½ |
-½ |
+½ |
-½ |
+½ |
+½ |
-½ |
+½ |
-½ |
+½ |
-½ |
+½ |
|
j |
½ |
½ |
½ |
1½ |
½ |
½ |
1½ |
1½ |
2½ |
½ |
½ |
1½ |
1½ |
2½ |
2½ |
3½ |
etc.