Wednesday, May 22, 2013

Four Quantum Numbers ... or This -- go ahead and click

There are four quantum numbers (n, l, ml, ms). No two electrons in the same atom can have the same four quantum numbers. Each quantum number describes a different aspect of the electron and its orbital. These numbers are obtained from the solution of the Schrödinger Equation for atoms in spherical coordinates.

n, the principle quantum number

n tells you about the size of the orbital.  It is related to how far the electron is from the atom.  It is also related to the energy of the electron. ncan be any positive integer number.  An orbital has n1radial nodes as well, which describe a radius at which the probability of finding the electron is 0.

l, azimuthal quantum number

lt tells you about the angular momentum of the electron in the orbital.  It defines the shape of the orbital.  lt can be any integer between (and including) 0 and (n1).  Each orbital has lplanar nodes.
Some examples of orbitals with different l:
l=0is an s orbital, with no planar nodes.
S orbitals.jpg
l=1gives a p orbital, which has one planar node.
p orbital 1.JPG 

ml, magnetic quantum number

ml tells you about the angular momentum projected on to the z axis. It tells you of the orientation of the orbital. It can be any integer between l and l.
l=1 has 3 different (but degenerate) ml possible values:-1,0 or 1. 
px orbital 1.JPG
py orbital 1.JPG
pz orbital 1.JPG

ms spin projection quantum number

mstells you about the spin of the electron.  An electron is a fermion, a type of quantum particle which is only allowed to have msequal to -1/2 or 1/2.