n = 1, 2, 3, 4, .
l = 0, 1, 2, 3, (n-1)
ml = -l, -l+1, -l+2, 0, ., l-1, l
You are familiar with these .
n is the integer number associated with an orbital
Different l values have different names arising from early spectroscopy
e.g., l =0 is labelled
l =1 is labelled
l =2 is labelled
l =3 is labelled etc .
Looked at another way .
n =1 l=0 ml=0 1s orbital (1 of)
n =2 l=0 ml=0 2s orbital (1 of)
l=1 ml=-1, 0, 1 2p orbitals (3 of)
n =3 l=0 ml=0 3s orbital (1 of)
l=1 ml=-1, 0, 1 3p orbitals (3 of)
l=2 ml=-2,-1,0,1,2 3d orbitals (5 of)
etc. etc. etc.
Hence we begin to see the structure behind the periodic table emerge.
Work out, and name, all the possible
orbitals with principal
quantum number n=5.
How many orbitals have n=5?
The radial wavefunctions for H-atom are the set of Laguerre functions in terms of n, l
-the most probable
orbital radius of an H-atom 1s electron.
The square of the wavefunction,
at a point is proportional to the
of finding the particle at that point.
Y* = Y
In 1D: If the amplitude of the wavefunction of a particle at some point x is Y(x) then the probability of finding the particle between x and x +dx is proportional to
(x)Y*(x)dx = (x)
Y* is the complex conjugate of Y.
At long distances from the nucleus, all wavefunctions decay to .
Some wavefunctions are zero at the nucleus (namely, all but the l=0 (s) orbitals). For these orbitals, the electron has a zero probability of being found .
Some orbitals have nodes, ie, the wave function passes through zero; There are such radial nodes for each orbital.