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.
There is not a numerical formula in the simplest sense, but there is a model
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 s-orbital can hold
two (2x1) electrons: one spin-up and one spin-down. A p-orbital can hold
six (2x3) electrons: three of each spin. A d-orbital can hold ten (2x5)
electrons. A d-orbital can hold fourteen (2x7) electrons. How the shells
map out is as follows:
Shell # of Electrons in Orbitals
s p d f
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 f-orbital. If you look
at a periodic table of elements, you will see a remarkable agreement with
this chart. Elements that end with s-orbital electrons are the first two
columns (except for Helium). Elements that end with p-orbitals are the six
right-most columns. D-orbital elements are the transition metals.
F-orbitals 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.
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.
The filling of atomic orbitals in an atom is based on the solution of
Schroedinger's equation for the H-atom. The wave functions [solutions]
depend on three quantum numbers: n, l, and m. The allowed values are:
l = 0,1,2,..., (n-1) 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
z-component of the angular momentum. This is not exactly true for
poly-electron atoms, but the it is qualitatively correct.
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Update: June 2012