CHM 501 Lecture

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
letter designation
 0
s
 1
p
 2
d
 3
f
 4
g

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
 
 
 

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, ml, ms)
 

Periodic Table: based on electron configurations and can be used to predict them but not absolute (electron configurations are experimental quantities)