The Periodic Table

The following table gives the electron configurations for the ground states of light atoms.

Z El. Electron Configuration \bgroup\color{black}$^{2s+1}L_j$\egroup Ioniz. Pot.
1 H \bgroup\color{black}$(1s)$\egroup \bgroup\color{black}$^2S_{1/2}$\egroup 13.6
2 He \bgroup\color{black}$(1s)^2$\egroup \bgroup\color{black}$^1S_0$\egroup 24.6
3 Li He \bgroup\color{black}$(2s)$\egroup \bgroup\color{black}$^2S_{1/2}$\egroup 5.4
4 Be He \bgroup\color{black}$(2s)^2$\egroup \bgroup\color{black}$^1S_0$\egroup 9.3
5 B He \bgroup\color{black}$(2s)^2(2p)$\egroup \bgroup\color{black}$^2P_{1/2}$\egroup 8.3
6 C He \bgroup\color{black}$(2s)^2(2p)^2$\egroup \bgroup\color{black}$^3P_0$\egroup 11.3
7 N He \bgroup\color{black}$(2s)^2(2p)^3$\egroup \bgroup\color{black}$^4S_{3/2}$\egroup 14.5
8 O He \bgroup\color{black}$(2s)^2(2p)^4$\egroup \bgroup\color{black}$^3P_2$\egroup 13.6
9 F He \bgroup\color{black}$(2s)^2(2p)^5$\egroup \bgroup\color{black}$^2P_{3/2}$\egroup 17.4
10 Ne He \bgroup\color{black}$(2s)^2(2p)^6$\egroup \bgroup\color{black}$^1S_0$\egroup 21.6
11 Na Ne \bgroup\color{black}$(3s)$\egroup \bgroup\color{black}$^2S_{1/2}$\egroup 5.1
12 Mg Ne \bgroup\color{black}$(3s)^2$\egroup \bgroup\color{black}$^1S_0$\egroup 7.6
13 Al Ne \bgroup\color{black}$(3s)^2(3p)$\egroup \bgroup\color{black}$^2P_{1/2}$\egroup 6.0
14 Si Ne \bgroup\color{black}$(3s)^2(3p)^2$\egroup \bgroup\color{black}$^3P_0$\egroup 8.1
15 P Ne \bgroup\color{black}$(3s)^2(3p)^3$\egroup \bgroup\color{black}$^4S_{3/2}$\egroup 11.0
16 S Ne \bgroup\color{black}$(3s)^2(3p)^4$\egroup \bgroup\color{black}$^3P_2$\egroup 10.4
17 Cl Ne \bgroup\color{black}$(3s)^2(3p)^5$\egroup \bgroup\color{black}$^2P_{3/2}$\egroup 13.0
18 Ar Ne \bgroup\color{black}$(3s)^2(3p)^6$\egroup \bgroup\color{black}$^1S_0$\egroup 15.8
19 K Ar \bgroup\color{black}$(4s)$\egroup \bgroup\color{black}$^2S_{1/2}$\egroup 4.3
20 Ca Ar \bgroup\color{black}$(4s)^2$\egroup \bgroup\color{black}$^1S_{0}$\egroup 6.1
21 Sc Ar \bgroup\color{black}$(4s)^2(3d)$\egroup \bgroup\color{black}$^2D_{3/2}$\egroup 6.5
22 Ti Ar \bgroup\color{black}$(4s)^2(3d)^2$\egroup \bgroup\color{black}$^3F_{2}$\egroup 6.8
23 V Ar \bgroup\color{black}$(4s)^2(3d)^3$\egroup \bgroup\color{black}$^4F_{3/2}$\egroup 6.7
24 Cr Ar \bgroup\color{black}$(4s)(3d)^5$\egroup \bgroup\color{black}$^7S_{3}$\egroup 6.7
25 Mn Ar \bgroup\color{black}$(4s)^2(3d)^5$\egroup \bgroup\color{black}$^6S_{3/2}$\egroup 7.4
26 Fe Ar \bgroup\color{black}$(4s)^2(3d)^6$\egroup \bgroup\color{black}$^5D_{4}$\egroup 7.9
36 Kr (Ar) \bgroup\color{black}$(4s)^2(3d)^{10}(4p)^6$\egroup \bgroup\color{black}$^1s_0$\egroup 14.0
54 Xe (Kr) \bgroup\color{black}$(5s)^2(4d)^{10}(5p)^6$\egroup \bgroup\color{black}$^1s_0$\egroup 12.1
86 Rn (Xe) \bgroup\color{black}$(6s)^2(4f)^{14}(5d)^{10}(6p)^6$\egroup \bgroup\color{black}$^1s_0$\egroup 10.7

We see that the atomic shells fill up in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p. The effect of screening increasing the energy of higher \bgroup\color{black}$\ell$\egroup states is clear. Its no wonder that the periodic table is not completely periodic.

The Ionization Potential column gives the energy in eV needed to remove one electron from the atom, essentially the Binding energy of the last electron. The Ionization Potential peaks for atoms with closed shells, as the elctron gains binding energy from more positive charge in the the nucleus without much penalty from repulsion of the other electrons in the shell. As charge is added to the nucleus, the atom shrinks in size and becomes more tightly bound. A single electron outside a closed shell often has the lowest Ionization Potential because it is well screened by the inner electrons. The figure below shows a plot of ionization potential versus Z.


The perodic table of elements is based on the fact that atoms with the same number of electrons outside a closed shell have similar properties. The rows of the periodic table contain the following states.
  1. 1s
  2. 2s, 2p
  3. 3s, 3p
  4. 4s, 3d, 4p
  5. 5s, 4d, 5p
Soon after, the periodicity is broken and special ``series'' are inserted to contain the 4f and 5f shells.

Jim Branson 2013-04-22