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The symbol ( ) indicates an unpaired electron in the outer shell, whereas the symbol ( ) indicates a pair of spin-up and -down electrons in an outer shell.
Electron configurations of electrons in an atom
Element Electron Configuration Spin Alignment
H 1 s 1 ( )
He 1 s 2 ( )
Li 1 s 2 2 s 1 ( )
Be 1 s 2 2 s 2 ( )
B 1 s 2 2 s 2 2 p 1 ( ) ( )
C 1 s 2 2 s 2 2 p 2 ( ) ( ) ( )
N 1 s 2 2 s 2 2 p 3 ( ) ( ) ( ) ( )
O 1 s 2 2 s 2 2 p 4 ( ) ( ) ( ) ( )
F 1 s 2 2 s 2 2 p 5 ( ) ( ) ( ) ( )
Ne 1 s 2 2 s 2 2 p 6 ( ) ( ) ( ) ( )
Na 1 s 2 2 s 2 2 p 6 3 s 1 ( )
Mg 1 s 2 2 s 2 2 p 6 3 s 2 ( )
Al 1 s 2 2 s 2 2 p 6 3 s 2 3 p 1 ( ) ( )

The maximum number of electrons in a subshell depends on the value of the angular momentum quantum number, l . For a given a value l , there are 2 l + 1 orbital angular momentum states. However, each of these states can be filled by two electrons (spin up and down, ). Thus, the maximum number of electrons in a subshell is

N = 2 ( 2 l + 1 ) = 4 l + 2 .

In the 2 s ( l = 0 ) subshell, the maximum number of electrons is 2. In the 2 p ( l = 1 ) subshell, the maximum number of electrons is 6. Therefore, the total maximum number of electrons in the n = 2 shell (including both the l = 0 and 1 subshells) is 2 + 6 or 8. In general, the maximum number of electrons in the n th shell is 2 n 2 .

Subshells and totals for n = 3

How many subshells are in the n = 3 shell? Identify each subshell and calculate the maximum number of electrons that will fill each. Show that the maximum number of electrons that fill an atom is 2 n 2 .

Strategy

Subshells are determined by the value of l ; thus, we first determine which values of l are allowed, and then we apply the equation “maximum number of electrons that can be in a subshell = 2 ( 2 l + 1 ) ” to find the number of electrons in each subshell.

Solution

Because n = 3 , we know that l can be 0, 1, or 2; thus, there are three possible subshells. In standard notation, they are labeled the 3 s , 3 p , and 3 d subshells. We have already seen that two electrons can be in an s state, and six in a p state, but let us use the equation “maximum number of electrons that can be in a subshell = 2 ( 2 l + 1 ) ” to calculate the maximum number in each:

3 s has l = 0 ; thus, 2 ( 2 l + 1 ) = 2 ( 0 + 1 ) = 2 3 p has l = 1 ; thus, 2 ( 2 l + 1 ) = 2 ( 2 + 1 ) = 6 3 d has l = 2 ; thus, 2 ( 2 l + 1 ) = 2 ( 4 + 1 ) = 10 Total = 18 ( in the n = 3 shell ) .

The equation “maximum number of electrons that can be in a shell = 2 n 2 ” gives the maximum number in the n = 3 shell to be

Maximum number of electrons = 2 n 2 = 2 ( 3 ) 2 = 2 ( 9 ) = 18 .

Significance

The total number of electrons in the three possible subshells is thus the same as the formula 2 n 2 . In standard (spectroscopic) notation, a filled n = 3 shell is denoted as 3 s 2 3 p 6 3 d 10 . Shells do not fill in a simple manner. Before the n = 3 shell is completely filled, for example, we begin to find electrons in the n = 4 shell.

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The structure of the periodic table ( [link] ) can be understood in terms of shells and subshells, and, ultimately, the total energy, orbital angular momentum, and spin of the electrons in the atom. A detailed discussion of the periodic table is left to a chemistry course—we sketch only its basic features here. In this discussion, we assume that the atoms are electrically neutral; that is, they have the same number of electrons and protons. (Recall that the total number of protons in an atomic nucleus is called the atomic number, Z .)

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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