

Orbital maximum
Name: Rajesh
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 20002001
Question:
Is there a formula for determining the maximum number of
electrons that each orbit of an atom can contain. I seem to recollect
that Neil Bohr had come up with this formula.
Replies:
There is not a numerical formula in the simplest sense, but there is a model
that works.
Each shell of electrons is divided into orbitals, based on angular momentum
and spin. There are four kinds of orbitals, often labeled "s", "p", "d",
and "f" (I believe these are based on Latin words). An sorbital can hold
two (2x1) electrons: one spinup and one spindown. A porbital can hold
six (2x3) electrons: three of each spin. A dorbital can hold ten (2x5)
electrons. A dorbital can hold fourteen (2x7) electrons. How the shells
map out is as follows:
Shell # of Electrons in Orbitals
s p d f
1 2
2 2 6
3 2 6 10
4 2 6 10 14
5 2 6 10 14
6 2 6 10 14
7 2 6 10 14
No naturally occurring atom has electrons beyond an forbital. If you look
at a periodic table of elements, you will see a remarkable agreement with
this chart. Elements that end with sorbital electrons are the first two
columns (except for Helium). Elements that end with porbitals are the six
rightmost columns. Dorbital elements are the transition metals.
Forbitals are the inner transition metals (La, Ac, ...). The shells tend
to fill in an order along diagonal lines: upper right to lower left. 1s;
2s; 2p,3s; 3p,4s; 3d,4p,5s; 4d,5p,6s; 4f,5d,6p,7s; and so on.
Mellendorf
I looked in all the reference books I have and could not locate such a
formula. You may try a graduate level quantum mechanics text...good luck.
Katie Page
The filling of atomic orbitals in an atom is based on the solution of
Schroedinger's equation for the Hatom. The wave functions [solutions]
depend on three quantum numbers: n, l, and m. The allowed values are:
n=1,2,3,...
l = 0,1,2,..., (n1) These are the s,p,d,f... orbitals.
m= 0, +/1, +/ 2, +/3,..., +/ l
In one electron atoms, the principal quantum number 'n' determines the
energy, the azimuthal quantum number 'l' determines the square of the
angular momentum, and the magnetic quantum 'm' determines the allowed
zcomponent of the angular momentum. This is not exactly true for
polyelectron atoms, but the it is qualitatively correct.
Vince Calder
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Update: June 2012

