Atomic Structure
Wave properties of electrons are constrained by certain boundary conditions:
1) the electron exists somewhere in space
2) the electron is continuous
3) the electron is finite
When these conditions are imposed upon Schroedinger’s equation, the
result is quantization
1) each electron can only have certain energies (energy quantization)
2) each electron can only occupy certain volumes of space (spatial
quantization)
Hydrogenic Wavefunctions:
quantization is described by a set of numbers called quantum
numbers:
n = principal quantum number, found only in R, distance dependence
l = orbital angular momentum, found in R and Y, orbital
shape
ml = magnetic quantum number, found only in
Y, orientation in space
The quantum numbers are mathematically related
n = 1, 2, 3, 4, ...
l = n-1, n-2, n-3, ..., 0
ml = -l, -l+1, -l+2,
..., l-2, l-1, l
The l quantum number is usually designated by a letter:
| l |
|
| 0 |
|
| 1 |
|
| 2 |
|
| 3 |
|
| 4 |
|
Experimental evidence (and relativistic theory) indicates the presence
of a fourth quantum
number, ms, the spin quantum number = ±1/2
Radial Wavefunctions:
Angular Wavefunctions:
General nodal properties:
total number of nodes = n-1
total number of planar (or angular) nodes = l
total number of radial nodes = n-l-1