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
m_{l} = magnetic quantum number, found only in
Y, orientation in space
The quantum numbers are mathematically related
n = 1, 2, 3, 4, ...
l = n1, n2, n3, ..., 0
m_{l} = l, l+1, l+2,
..., l2, l1, 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, m_{s}, the spin quantum number = ±1/2
Radial Wavefunctions:
Angular Wavefunctions:
General nodal properties:
total number of nodes = n1
total number of planar (or angular) nodes = l
total number of radial nodes = nl1
Multielectron atoms: can't solve the Schroedinger equation exactly
so assumptions must be made; assume the hydrogenic obitals are adequate
and electrons occupy them in some fashion
Two guiding principals used to account for electron configurations
Aufbau Principle: electrons occupy orbitals in such a manner to give the lowest possible total energy
Pauli Exclusion Principle: each electron in an atom is described
by a unique set of quantum numbers (n, l,
m_{l}, m_{s})
Periodic
Table: based on electron configurations and can be used to predict
them but not absolute (electron configurations are experimental
quantities)