## Effective Nuclear Charge

The next thing to be considered is effective nuclear charge. Generally speaking, effective nuclear charge is the charge felt by the valence electrons after you have taken into account the number of shielding electrons that surround the nucleus.

Again let's take a look at a fluorine atom. (Also note example 5b in your workbook.) The nucleus itself has a +9 charge and anything in its vicinity will feel that charge. The two electrons in the first energy level as they look at the nucleus feel a +9 charge because that is the charge on the nucleus. But the electrons that are in the valence energy level would be shielded from the nucleus by the 2 shielding electrons. The +9 nuclear charge is shielded by 2 electrons to give an effective nuclear charge of +7 that is felt by the valence electrons. If you get out beyond the valence electrons, then the effective charge is 0 simply because the +9 charge of the nucleus is surrounded by 9 electrons.
 nuclear charge shielding electrons valence electrons F +9 1s2 2s22p5 2 7 +7 7 effective nuclear charge

Generally we are only concerned with the effective nuclear charge as it pertains to the valence electrons (+7 in this case), but sometimes the broader concept of what charge is felt by other electrons is useful.

### Practice

With that in mind, figure out what the effective nuclear charge would be for neon and sodium for the electrons in each energy level. What would the first two electrons feel? What would the next eight electrons feel? Then for sodium, what would that last electron feel? So take a moment to figure that out. (Refer to ex. 5.b. in your workbook, if that helps.)

 What charge is felt by the electrons in the first level of a neon atom? What charge is felt by the electrons in the second level (valence level) of a neon atom? What charge is felt by the electrons in the first level of a sodium atom? What charge is felt by the electrons in the second level of a sodium atom? What charge is felt by the electrons in the third (valence) level of a sodium atom?

 What charge is felt by the electrons in the first level of a neon atom? 10 What charge is felt by the electrons in the second (valence) level of a neon atom?  8 What charge is felt by the electrons in the first level of a sodium atom?  11 What charge is felt by the electrons in the second level of a sodium atom?  9 What charge is felt by the electrons in the third (valence) level of a sodium atom?  1

### Effective Nuclear Charge - Continued

For neon you should have figured that the electrons in the first energy level would feel a nuclear charge of +10, the full nuclear charge. Then the 8 valence electrons would feel a +8 effective nuclear charge. Going on down to sodium, the first 2 electrons would feel a +11 nuclear charge. The 8 electrons in the second energy level would feel a +9 effective nuclear charge. The one valence electron would feel a +1 effective nuclear charge.

Notice what happens. As you go across the table from fluorine to neon, the effective nuclear charge felt by the valence electrons increases. Then as you go to sodium in the next period, there is another energy level, the number of shielding electrons increases, causing the effective nuclear charge felt by the valence electron to drop.
 Effective Nuclear Charge for Valence Electrons F Ne Na +7 +8 +1

Notice that in all these examples the effective nuclear charge is the same as the number of valence electrons. That is true as long as you are dealing with neutral atoms. However many valence electrons there are, that will be the effective nuclear charge that the valence electrons feel. It has to be that way for neutral atoms. It is not true when dealing with ions.

Also notice that the effective nuclear charge depends on both the nuclear charge and the number of shielding electrons. The nuclear charge keeps increasing. Meanwhile, the shielding electrons stay constant while you are going across s and p parts of the period, (but increase gradually across the d part of the period). Then when you go to the next period, they jump in number. Consequently, the effective nuclear charge drops at that point. Therefore, the effective nuclear charge increases as you go across a period and then drops and starts over again at +1 when you start the next period. Within a period the effective nuclear charge increases as you go across the periodic table.

As you go down a group, the increase in the nuclear charge is cancelled out by the increase in shielding electrons and the effective nuclear charge stays pretty much the same. In carbon the 4 valence electrons in the outermost shell feel a +6 charge surrounded by two shielding electrons for a +4 effective nuclear charge. For silicon it would also be a +4 effective nuclear charge because the 14 protons in the nucleus are surrounded by 10 shielding electrons. Germanium (Ge) has 32 protons and it has 28 shielding electrons and so the valence electrons feel an effective nuclear charge of +4. As you go down a group, the increase in the nuclear charge is balanced by an increase in the number of shielding electrons so that the effective nuclear charge remains the same.
 nuclear charge shielding electrons effective nuclear charge C +6 2 +4 Si +14 10 +4 Ge +32 28 +4

One other thing I should mention about the effective nuclear charge is that it is quite often referred to as the kernel charge. The "kernel" includes the nucleus and all shielding electrons but does not include the valence electrons.

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