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Name: Rajesh
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 2000-2001

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 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 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
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 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.

Katie Page

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.

Vince Calder

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