Models of Atoms
•
Just like a particle in a box, an electron is confined to the atom.
Therefore, its wavefunction has to obey certain boundary conditions.
Just like the particle in a box, this results in quantized energy or
discrete energy levels.
•
Schrödinger solved his own equation to find the actual energy levels
in a hydrogen atom.
He inserted the expression for the potential
energy of the electron as:
V(r) =
e
2
/(4πε
0
r) and was able to solve the
equation to get:
E
n
= h
R
/n
2
R =
3.29 x 10
15
Hz (same as Rydberg’s empirical
equation!!)
•
For other species with one electron, this expression becomes:
E
n
= (Z
2
h
R
)/n
2
•
The Integration of the Schrödinger equation, gives a set of four
numbers, the quantum numbers (n, l, m
l
, and s).
Each electron around
the nucleus has its own set of quantum numbers that distinguishes it
from each and every other electron in the same atom.
THE FOUR QUANTUM NUMBERS
Principle Quantum Number, n:
It corresponds to the main energy level.
The principle quantum number is the volume of space in which an electron
moves around a nucleus. The allowed values for n are:
n = 1,2,3,4,...
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 Fall '07
 Fakhreddine/Lyon
 Electron, Atomic orbital, Principal quantum number, Azimuthal quantum number

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