Periodic Trend: Effective Nuclear Charge - Video Tutorials & Practice Problems
Effective Nuclear Charge (Zeff) measures the force exerted onto an electron by the nucleus.
Periodic Trend: Effective Nuclear Charge
Higher the Effective Nuclear Charge (ZEff), greater the attractive force, which results in electrons being pulled closer to the nucleus.
Higher the Shielding Constant (S), greater the repulsive force between valence and inner core electrons, which results in valence electrons pushed away from the nucleus.
Periodic Trend: Effective Nuclear Charge
Now the attractive force between electrons and the nucleus is influenced by shell number and the quantity of electrons. Now we can say here that as you increase the shell number of an atom, you're going to increase the distance between electrons and nucleus. Because remember the more shells you add, the further and further away they are from the nucleus and the further the electron is away from the nucleus than the lower the attractive force between them.
Now, we can also say that as you increase the quantity of electrons within the same shell or subshell, this would actually increase the attractive force because you're adding more electrons. But the distance the electrons are from the center from the nucleus is not increasing. So there's a building and more attraction between the electrons and the nucleus.
Now in general, the periodic trend for effective nuclear charge is that it increases as you're moving from left to right across a period and up and going up a group. So as we're heading to the top right corner of the periodic table, we expect our effective nuclear charge to increase. So just remember that general pattern for effective nuclear charge.
Moving towards the top right corner of the Periodic Table causes effective nuclear charge to increase.
Periodic Trend: Effective Nuclear Charge Example 1
Here, it says, "Which of the following represents a chalcogen with the greatest effective nuclear charge?" Remember, a chalcogen is an element that is in Group 6A. So what we have to do here is figure out which element or elements are in Group 6A.
If we take a look, we have chlorine, lithium, sulfur, selenium, and neon. The only elements from this list that are in Group 6A are sulfur and selenium. Remember, the general trend is as we head towards the top right corner of the periodic table, our effective nuclear charge is going to increase.
So here, we have sulfur, which is in Group 6A. A few spaces below it is selenium. So, based on this trend, as we move up a group, effective nuclear charge should increase. That would mean that sulfur would be the chalcogen with the greatest effective nuclear charge from the options provided.
Periodic Trend: Effective Nuclear Charge
Here we take a simple approach to calculate the effective nuclear charge of a valence electron. When only given the shell number, remember your shell number uses the variable n, which stands for the principal quantum number.
Now here we have the atomic view of the aluminum atom. Aluminum is in group 3A. It has an atomic number 13. Here we say that it is 1s2 2s2 2p6 3s2 3p1 for its electron configuration.
Its effective nuclear charge formula, which is simply the effective nuclear charge, which is Zeff = the atomic number of the element minus its shielding constant s. Now here the shielding constant could be seen as the inner core electrons for the given element.
So, we use this simplified version of the effective nuclear charge when we only have the shell number.
Periodic Trend: Effective Nuclear Charge Example 2
So here we're gonna answer this example question. Based on the image we have above here, it says, what is the effective nuclear charge felt by an electron in the third shell of an aluminum atom? The steps we take is we find the element and its atomic number on the periodic table. Here, we already know that aluminum has an atomic number 13. We're going to write the condensed electron configuration and determine its number of inner core electrons.
So if we wanted to do the condensed electron configuration instead of writing all of this, we would just write it as neon, followed by 3s23p1. Here, remember, our inner core electrons are just the electrons that are not on the outer shell. So here we can see that since it's in group 3A, it has three valence electrons. It has a total of 13 electrons, though, so you do 13 minus 3, and that difference will be the number of inner core electrons. So it has 10 inner core electrons.
Now we're gonna use the atomic number and the shielding constant to determine the effective nuclear charge. So here we say that the effective nuclear charge felt by an electron in the third shell of an aluminum atom equals Z minus S. So that's 13, the atomic number, minus its shielding constant, which remember, is equal to the number of inner core electrons. So that's 10. So that equals plus three. That means an electron in the third shell would feel a plus three effective nuclear charge or attractive force from the nucleus.
So this is a simplified way of looking at the effective nuclear charge of any electron within a given atom.
What is the identity of an element when the effective nuclear charge of its valence electrons is 18 while its shielding constant is 5?
Periodic Trend: Effective Nuclear Charge Example 3
Now here, we're going to use Slater's rule to determine our new, effective nuclear charge. Slater's rule is just a system used to determine the effective nuclear charge of a specific electron within an orbital. So we're given just more than the shell number for our electron. For this example, it says, using Slater's rules, calculate the effective nuclear charge of a 3p orbital electron in calcium.
Step one is we're gonna group the electrons in an electron configuration in order of increasing n value and in this form, so calcium would be here on the periodic table if electron configuration will be 1s2 2s2 2p6 3s2 3p6. We haven't gotten to 3d with it. So we skipped 3d for us to here. We have listed it in order in order of increasing n value. So this would be n equals 1, n equals 2, and n equals 3. 3d is also n equals 3, but 3s and 3p orbitals are similar because they're in the same row of the periodic table. So we group them together 3d is its own separate row. And if we have f, it would be its own separate thing as well. Then we have 4s and 4p, which are n equals 4. 4d is here separate from 4s and 4p, and then 4f is also separate because it's in its own row. This would be 5, and this would also be 5.
Now this is important. We have to identify an electron within the selected electron group we're asked to find the effective nuclear charge of a 3p electron. So it's here somewhere in here. We're gonna use the lower electron groups to the left to determine the calculated shielding constant because remember, the electrons in front are the ones protecting that electron from the full blast of the nucleus. Ignore higher electron groups. Those to the right, they don't shield us. So the electron we're looking at is this one. It's being shielded from the full effect of the nucleus by the electrons that are lower than it, these ones in orange. It's also being partially protected by the electrons in the same shell, viz the ones in yellow.
Now we're gonna use the calculated shielding constant of the electron to determine the effective nuclear charge, so the calculated shielding constant equals the electrons within your electron group times Slater's constant plus, adding up all of the lower electrons, the ones to the left of our electron times, their Slater's constant here. All of this will help us to calculate the shielding constant using Slater's rule.
All right, So how does this work well for S and P electrons? We're gonna say electrons in the same group, their slayers constant is equal to 35. If it's an end minus one group, then each electron is 85. And if its end minus two or greater than its 1. for DNF, if they're in the same group, it would be 35. And then if it's lower than that, then we would say here that it is 0.85.
Then here it's s count equals your atomic number minus You're Slater's constant. So let's see how it work here n equals one here n equals to hear n equals three. And here n equals four. We're looking at one of these electrons here, so we'd say within there. There are a total off eight electrons, right? And we're looking at one of them. So that means there's seven other electrons in my same group with me. Each one of them is 10.35 which comes out to 2. and minus one.
So one n value lower than me are these electrons here and there are eight of them total. Each of them contributes 0.85 when its n minus one. So that comes out to 6.80 Then finally, groups that our n minus two or greater, which is this one here. This one has two electrons within it. So that's two times 1.0 The total value here we get is 8.11 points are 11.25
So for calcium, we'd say that it's effective nuclear charge, which is s Cal equals it atomic number, which on the periodic table is 20 minus what we just found here for our sliders constant 11.25 Plugging all that in means that we're gonna feel in effect of 8.75 as the effective nuclear charge for calcium. So this is what the calcium electron within the three p electron orbital will feel in terms of the attractive pull of the nucleus, so it could be a little bit complicated. But this is the approach we have to take when they're giving us more specific information on an electron within a given orbital.
In which orbital does an electron in a sulfur atom experience the greatest shielding?
Using Slater's Rules calculate the effective nuclear charge of the 4d orbital electron in iodine.
26.1%
31.8%
70.1%
72.7%
82.1%
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