Bootcamp GC - Periodic Trends Question

[Leo Messi]

I was working on the Bootcamp section specific tests and I ran into this:





3. Calcium has a larger atomic radius than magnesium because of the:

E. Increase in electron shielding

First, almost all of the periodic trends can be derived from the two concepts of effective nuclear charge and electron shielding. In a given group in the periodic table, the effective nuclear charge stays relatively constant due to the constant number of valence electrons; the increasing number of protons is balanced with an increasing number of core electrons. The effective nuclear charge is responsible for the decrease in atomic size across periods.
The electron shielding effect reduces the effect of a full nuclear charge. As more core electrons are added, they begin to “shield” the valence electrons from the increasingly positive nucleus. This allows the outer electrons to move farther away from the nucleus, hence increasing atomic size. The electron shielding effect is responsible for the increase in atomic size moving down groups.

Topic: Periodic Properties and Trends




So they said that going down a column, the electron shielding effect is responsible for the increased size and that going right in a row, the effective nuclear charge is responsible for the decrease in size. I'm confused about this because I always thought that even though when you go down a column, it is true that you will have more electron shielding (more orbitals are filled) but don't you also have more protons in the nucleus? So with the same number of valence electrons, you would be further out but there also will be a stronger charge? Thanks for any input!

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[DAT Destroyer]

I was working on the Bootcamp section specific tests and I ran into this:





3. Calcium has a larger atomic radius than magnesium because of the:

E. Increase in electron shielding

First, almost all of the periodic trends can be derived from the two concepts of effective nuclear charge and electron shielding. In a given group in the periodic table, the effective nuclear charge stays relatively constant due to the constant number of valence electrons; the increasing number of protons is balanced with an increasing number of core electrons. The effective nuclear charge is responsible for the decrease in atomic size across periods.
The electron shielding effect reduces the effect of a full nuclear charge. As more core electrons are added, they begin to “shield” the valence electrons from the increasingly positive nucleus. This allows the outer electrons to move farther away from the nucleus, hence increasing atomic size. The electron shielding effect is responsible for the increase in atomic size moving down groups.

Topic: Periodic Properties and Trends




So they said that going down a column, the electron shielding effect is responsible for the increased size and that going right in a row, the effective nuclear charge is responsible for the decrease in size. I'm confused about this because I always thought that even though when you go down a column, it is true that you will have more electron shielding (more orbitals are filled) but don't you also have more protons in the nucleus? So with the same number of valence electrons, you would be further out but there also will be a stronger charge? Thanks for any input!

Flummoxing indeed, why does this need to be complicated? As you go down a group, size increases as more principle energy levels are involved,,,,,,Across the table we decrease in size due to a greater number of protons ( atomic number ) acting on the electron.

Consult any Chemistry book written by a PhD for further clarity.....Zumdahl, Chang, and Brown-LeMay are excellent.

Hope this helps..

 

[FeralisExtremum]

I'll try my best to help with this. It's a bit confusing because effective charge and shielding are technically integrated and I have to add the caveat that this is all an oversimplification for the basic level of understanding sufficient for the DAT.

Effective nuclear charge, also known as Zeff, uses the formula:

Z represents the number of protons (as you said, it will increase as we go down a column, or across a row). S is the number of inner shell electrons that contribute to shielding. If you need an example of the formula being applied to the valence electron of an example atom:

Now to address the issue: as we go across a period, our Zeff increases (and our atomic radius therefore decreases) because we are increasing our number of protons but the inner electron count remains the same throughout the entire period. So the Zeff for Carbon is 6 - 2 =4, Nitrogen 7 - 2 = 5, Oxygen 8 - 2 = 6, etc. Notice that the valence electrons of any atoms in the same shell (i.e. in the same period) are expected to be roughly the same distance away from the nucleus, so we can use Zeff as an indicator of radius pretty effectively.

But going down groups, using our formula, we would expect Zeff to not change. Yes, going down a group you have more protons, but you also have an entirely new shell of inner e- contributing to the shielding, and it more or less cancels out. Applying Zeff to a few valence electrons of elements in the same group:

This raises the question: if Zeff is the same as we go down a group*, why does our atomic radii get bigger? The simple explanation is that these electrons are being added to additional electron shells further and further away from the nucleus, so the Zeff experienced by these outermost electrons is reduced due to the increase in distance - not so much the shielding as Qvault says (maybe it could be rationalized as shielding if outer valence electron shells are further way due to electron shielding/repulsion from inner electrons in the first place?). If you wanted an even more in depth explanation, look at Coulomb's Law applied to atoms:

As we noted above, the distance for electrons being added to the same shell (i.e. atoms in the same row) is effectively the same, so we could ignore the distance and just look at Zeff and that's enough to approximate the atomic radii trend. But for atoms in different rows, that assumption of ignoring distance is no longer valid - accounting for the increased distance (and Zeff staying roughly the same), the formula shows us why the attractive force between the nucleus and valence electrons decreases moving down groups (result: larger radius).

All sorts of caveats:
* Zeff actually increases slightly going down a group. This seems counter-intuitive and understanding periodic trends with that in mind will simply confuse you, so don't worry about it.
* Zeff is an oversimplified formula, doesn't account for all the important factors
* Unlike what the Zeff formula implies, electrons in the same electron shell do repel each other, but only slightly.
* Electron shells aren't actually the round orbits as portrayed in the image above and examples given. They occupy quantum orbital shapes where electrons are technically more likely to exist.

Got way longer than I expected, but hope it helps.

 

[ns718]

Flummoxing indeed, why does this need to be complicated? As you go down a group, size increases as more principle energy levels are involved,,,,,,Across the table we decrease in size due to a greater number of protons ( atomic number ) acting on the electron.

Consult any Chemistry book written by a PhD for further clarity.....Zumdahl, Chang, and Brown-LeMay are excellent.

Hope this helps..

Thank youuuu. This makes it a lot simpler to remember and understand

 

[Leo Messi]

Thank you guys so much! I knew it was a really simple concept and I understood it before, but going through the exam, I was just getting everything mixed up. Thanks again for the help!