# Relationship between Zeffective and Radius

## Main Question or Discussion Point

When you go across a period the radius generally increases. Does that mean that the z effective decrease? If Z effective is the strength (pull) the valence electron feels, that should be the case, shouldn't it? The electrons in the lower n-orbitals should screen it from being pulled to the positive nucleus, right?

Am I wrong?

Borek
Mentor
You can use http://en.wikipedia.org/wiki/Slater's_rules to calculate Zeffective and check for yourself.

Note that you have mentioned only changes to Zeffective, but you have ignored fact that number of electrons grows across the period. There are several opposing trends present - one is increase in Z, the other is changes in screening, and the last one number of electrons. Final outcome is that radius grows, but it is not that easy to predict using simplified rules, they do their best when used to compare atoms/ions that are otherwise identical and differ only by one factor.

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You can use http://en.wikipedia.org/wiki/Slater's_rules to calculate Zeffective and check for yourself.

Note that you have mentioned only changes to Zeffective, but you have ignored fact that number of electrons grows across the period. There are several opposing trends present - one is increase in Z, the other is changes in screening, and the last one number of electrons. Final outcome is that radius grows, but it is not that easy to predict using simplified rules, they do their best when used to compare atoms/ions that are otherwise identical and differ only by one factor.

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Wait, I thought the radius only grows if there is another N number added e.g. n=1 n=2, you know shells? Or can adding another orbital actually increase the size of a radius?

I forgot about the increasing electrons,that certainly has an affect.

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Borek
Mentor
Wait, I thought the radius only grows if there is another N number added e.g. n=1 n=2, you know shells?
That would mean all atoms in one period have identical radius.

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methods

Thanks, that makes sense now!

When you go across a period the radius generally increases.
Assuming you mean going from left to right, then the trend is that the radius decreases. The radius decreases because the effective nuclear charge increases.

Here's the AP Chem level explanation:

As you move across a period, the atomic radius increases. This is because Zeffective decreases. The reason for this is in the orbitals:

As I move one step across a period, I gain one proton and one electron, and so IF all of the electrons were equidistant from the nucleus, theoretically the radius would remain the same (I gained an equal number of protons and electrons). But instead of being equidistant, electrons within an energy level are localized into orbitals. The net effect of localization is that inner orbitals "shield" outer orbitals from the nucleus, decreased the effective nuclear charge acting on the outer orbitals and keeping them from being pulled in as effectively (thus increasing the radius).

Keep in mind that this is all within the same period, and thus energy level.

If we look at the data for the van der Waal's radii (Bondi J. Phys Chem 1964, 68, 441):

C 170 pm
N 155 pm
O 150 pm
F 155 pm

Si 210 pm
P 185 pm
S 180 pm
Cl 180 pm

we see that the trend is decreasing radius as one moves from left to right across the periodic table. The data for the covalent radii show the same trend. If we look at the value of Slater's effective nuclear charge we see that it increases across the table. Clearly there is an inverse relationship between radius and effective nuclear charge.