0.2 The structure of an atom  (Page 5/6)

The answer is that we must consider also the distance of the electrons from the nucleus. Since it requires muchless energy to ionize a Sodium atom than to ionize a Neon atom even though Sodium's nuclear charge is greater, it must be thatthe electron which we remove from a Sodium atom is much farther from the nucleus than the electron in the Neon atom. We can makethe same comparison of the electrons removed during ionization of Neon and Argon atoms: the Argon electron must be farther from thenucleus than the Neon electron.

On the other hand, since the ionization energy fairly smoothly increases as we move from Lithium to Neon in thesecond period of elements, this reveals that the electrons are increasingly attracted to the nucleus for greater nuclear chargeand suggests that the electrons' distance from the nucleus might not be varying too greatly over the course of a single periodof the table.

If we follow this reasoning, we can even estimate how far an electron might typically be from the nucleus byusing our crude approximation that the ionization energy is equal to the negative of the Coulomb potential and solving for $r$ for each atom. This gives an estimate of distance of the electron from thenucleus:

Values of $r_{\mathrm{shell}}$ calculated in this way are shown for the first 20 elements here . Also shown for comparison is the ionization energy for these elements. Notice thatthe approximate distance of the electrons from the nucleus increases in steps exactly coinciding with the increases and dipsin the ionization energy.

Although these distances we have calculated do not have a precise physical meaning, this figure suggests a significant conclusion. The electrons in the elements are arranged into"shells" of increasingly greater distance from the nucleus. Hydrogen and Helium, with one and two electrons, haveionization energies consistent with electrons at similar and close distance from the nucleus. Then the second row elements lithiumthrough neon have virtually identical sizes, though larger than that for the first two elements. The third row elements, sodiumargon, have an approximate electron-nuclear distance which fluctuates a bit but is consistently larger than the second rowelements.

Because the sizes of the atoms appear to grow in steps which correspond exactly to the periods of the PeriodicTable, it seems that the electrons in the atoms are grouped into sets which are differing distances away from the nucleus. The firsttwo electrons, as in Helium, are close to the nucleus, whereas additional electrons, as in Lithium to Neon, are farther from thenucleus than the first two. The suggests that, for atoms Lithium to Neon, the first two electrons are in an inner "shell",and the remaining electrons are in an outer "shell."

We can refine this shell model for the electrons in an atom with further analysis of ionization energies.We can remove any number of electrons in sequence, forming ions with greater charge. We have been examining the first ionizationenergy, ${\mathrm{IE}}_1$ , but each successively removed electron has successively greater ionization energy: