Periodic Trend: Effective Nuclear Charge: Videos & Practice Problems

In an atom, electrons are subject to two key forces: attraction to the positively charged nucleus and repulsion from other negatively charged electrons. The effective nuclear charge ($Z$_eff) quantifies the net attractive force experienced by an electron from the nucleus, accounting for the repulsion by inner electrons, known as the shielding effect. As $Z$_eff increases, electrons are drawn closer to the nucleus. The periodic trend for $Z$_eff increases across a period (left to right) and up a group in the periodic table. Calculating $Z$_eff for a valence electron can be simplified to:

$Z$_eff = atomic number - shielding constant

where the shielding constant represents the number of inner core electrons. This concept is vital in understanding atomic structure and trends across the periodic table.

Effective Nuclear Charge

Now, within an atom, an electron experiences 2 different forces. It experiences an attraction by the nucleus and a repulsion by surrounding electrons. So let's say that we're examining this electron here. Well, the electron here is negatively charged, so it would form an attraction to the nucleus here, which is positively charged. At the same time, this outer electron here, since it's also negative, would repel this highlighted electron. So these electrons are experiencing these two different forces at the same time, attraction for the nucleus, but repulsion from one another.

Now effective nuclear charge, abbreviated as Zef, is the measurement of attractive force between protons and electrons. So here the attractive force between that electron and the nucleus can be explained by the effective nuclear charge. We're going to say here that the greater the effective nuclear charge than the greater the attractive force between the nucleus and the electron. And if you're attracted to one another, you're going to come closer together. So the electrons are going to be pulled closer to the nucleus.

At the same time we have our shielding constant. Now our shielding constant is the measurement is the measurement of the repulsive force between our valence electrons, so our outer shell electrons and the inner core electrons. Here we're going to say as that increases, that's going to cause an increase in the repulsive force. So valence electrons are going to be pushed further away from the nucleus. Here this electron in blue is experiencing a pushing away because the electron that's highlighted is repelling it further and further away from the nucleus. So just keep in mind we have these two forces at work within any given atom.

Effective Nuclear Charge Trends

Now the attractive force between electrons in 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 then 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.

Effective Nuclear Charge Example

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, tellurium, and neon. The only elements from this list that are in Group 6A are sulfur and tellurium. Remember the general trend is as we head towards the top right corner of the periodic table, effective nuclear charge is going to increase.

So here we have sulfur which is in Group 6A. Below it, a few spaces below it is tellurium. 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.

Effective Nuclear Charge Calculation

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 of 13. Here we say that it is 1 S 2²2S²2P⁶3S²3P¹ for its electron configuration.

Its effective nuclear charge formula, which is simply be effective nuclear charge which is Z_ef equals the atomic number of the element minus its shielding constant's. Now here the shielding constant can 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.

Effective Nuclear Charge Calculation Example

So here we're going to 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. So 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 of 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, we'd say here. Remember, our inner core electrons are just the electrons that are not on the outer shell. 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 - 3, and that difference would be the number of inner core electrons. So it has 10 inner core electrons. Now we're going to use the atomic number and the shielding constant to determine the effective nuclear charge. So here we'd say that the effective nuclear charge felt by an electron in the third shell of aluminum atom equals Z - S.

So that's 13 for 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 +3. That means an electron in the third shell would feel a +3 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?

• A. P
• B. Ar
• C. N
• D. V
• E. Al

Answer: (D)

Effective Nuclear Charge Calculation with Slater's Rules

Now here we're going to use Slater's rule to determine our new effective nuclear charge. Now 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.

So step 1 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, Its electron configuration would be 1s², 2s², 2p⁶, 3s²3p⁶. We haven't gone to 3d with it so we skip 3d4s². Here we've listed it in order in in order of increasing n value. So this would be 1 because 1 here, this would be n equals 2, n equals 3. 3d is also n equals 3, but 3 the s and p 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 electron. So it's here, somewhere in here. 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 shield as it, the ones in yellow. Now we're gonna use the calculated shield constant of the electron to determine the effect of nuclear charge. So the calculated, shielding constant equals the electrons within your electron group times our our 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.

Alright. So how does this work? Well, for s and p electrons we're gonna say electrons in the same group, their slayer's constant is equal to 0.35. If it's an n minus one group then each electron is 0.85, and if it's n minus 2 or greater then it's 1.0. For DNF, if they're in the same group, it would be 0.35, and then if it's lower than that, then we would say here that it is, point 85. Then here it's s count equals your atomic number minus your Slater's constant. So let's see how it would work.

Here n equals 1, here n equals 2, here n equals 3, and here n equals 4. We're looking at one of these electrons here. So let's say within there, there are a total of 8 electrons. Right? And we're looking at one of them. So that means there are 7 other electrons in my same group with me. Each one of them is 0.35, which comes out to 2.45. N minus 1, so one n value lower than me are these electrons here. And there are 8 of them total. Each of them contributes 0.85 when it's n minus 1. So that comes out to 6.80. Then finally, groups that are n minus 2 or greater which is this one here, this one has 2 electrons within it. So that's 2 times 1.00. The total value here we get is 8.0, 11 point sorry, 11.25.

So for calcium, we'd say that it's effective nuclear charge, which is s cal equals its atomic number, which on the periodic table is 20, minus what we just found here for our Slater's constant, 11.25. Plugging all that in means that we're gonna feel an effect of 8.75 as the effective nuclear charge for calcium. So this is what the calcium electron within the 3p electron orbital will feel in terms of the attractive pull of the nucleus. So it can 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?

• A. 2p
• B. 2s
• C. 3p
• D. 3s
• E. 1s

Answer: (C)

Rank the following elements by effective nuclear charge, Z_Eff, for a valence electron: Kr, Se, Ca, K, Ge

• A. K < Ca < Ge < Kr < Se
• B. K < Ca < Ge < Se < Kr
• C. Ca < K < Ge < Se < Kr
• D. Ca < K < Se < Ge < Kr

Answer: (B)

Using Slater's Rules calculate the effective nuclear charge of the 4d orbital electron in iodine.

• A. 26.1%
• B. 31.8%
• C. 70.1%
• D. 72.7%
• E. 82.1%

Answer: (A)

Here’s what students ask on this topic:

What is effective nuclear charge?

Effective nuclear charge, often symbolized as _Zeff, is the net positive charge experienced by an electron in a multi-electron atom. The concept is used to help explain the electron's attraction towards the nucleus in the presence of other electrons. In a simple view, the effective nuclear charge is the actual nuclear charge (the number of protons in the nucleus, Z) minus the shielding effect caused by the electrons located between the nucleus and the electron in question.

The shielding effect occurs because the inner electrons repel the outer electrons due to their negative charge, reducing the full nuclear charge's pull on those outer electrons. As a result, the effective nuclear charge is less than the actual nuclear charge. It increases across a period on the periodic table because the number of protons increases, but the shielding effect increases only slightly. This concept is crucial for understanding trends in atomic size, ionization energy, and other properties of elements.

How do you calculate effective nuclear charge?

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The effective nuclear charge (often symbolized as $Z_{\text{eff}}$ or $Z^{*}$) is the net positive charge experienced by an electron in a multi-electron atom. The concept is used to help explain the electron configuration of atoms, their sizes, and their ionization energies among other properties.

To calculate the effective nuclear charge, you can use Slater's rules, which provide a way to estimate the screening effect due to inner-shell electrons. Here's a simplified way to calculate it:

1. Determine the number of protons in the nucleus (atomic number, $Z$).
2. Estimate the shielding effect of the electrons between the nucleus and the electron for which you are calculating $Z_{\text{eff}}$. This is done by considering the number of electrons in inner shells and the same shell but at lower energy levels.
3. Subtract the shielding constant (S) from the actual nuclear charge (Z) to get the effective nuclear charge:

$Z_{\text{eff}}=Z-S$

The shielding constant (S) is found by applying Slater's rules, which assign different values to electrons in different orbitals and shells based on their ability to shield each other from the nuclear charge. The rules are specific and detailed, so you'll need to refer to them to get the exact value for S.

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Why does the effective nuclear charge increase across a period?

The effective nuclear charge (often symbolized as _Zeff or _Z*) is the net positive charge experienced by an electron in a multi-electron atom. This charge increases across a period on the periodic table due to the addition of protons in the nucleus as you move from left to right. Each additional proton increases the overall positive charge of the nucleus, which in turn attracts the negatively charged electrons more strongly.

However, while the number of protons increases, the number of inner-shell electrons, which serve to shield the outer electrons from the full charge of the nucleus, remains relatively constant across a period. This means that as you move across a period, the added electrons enter the same principal energy level without a significant increase in electron shielding. As a result, the outermost electrons are pulled closer to the nucleus, and the effective nuclear charge that they experience increases. This increasing _Zeff is responsible for trends across a period, such as decreases in atomic radius and increases in ionization energy, electronegativity, and electron affinity.

Why does the effective nuclear charge decrease down a group?

The effective nuclear charge (_Zeff) is the net positive charge experienced by an electron in a multi-electron atom. The concept arises from the fact that the electrons in the inner shells shield the outer electrons from the full charge of the nucleus due to electron-electron repulsion.

As you move down a group in the periodic table, the number of electron shells increases. Each additional shell adds a layer of electrons that shield the outer electrons from the nucleus. This increased shielding causes the outermost electrons to experience a lower effective nuclear charge. In other words, the pull from the nucleus on these outer electrons weakens because there are more inner electrons to counteract it.

Additionally, as the principal quantum number (n) increases, the distance between the nucleus and the outermost electrons also increases. Since the force of attraction between charged particles decreases with distance (as per Coulomb's law), the effective nuclear charge felt by the outer electrons is reduced. This is why, despite the increase in the actual nuclear charge due to the addition of protons in the nucleus, the effective nuclear charge experienced by the valence electrons decreases down a group.

What is the shielding constant?

The shielding constant, often symbolized by the letter "σ" (sigma), is a value used in chemistry to describe the decrease in the effective nuclear charge on an electron caused by electron-electron repulsion. Essentially, it's a measure of how much the attraction between an electron and the nucleus is reduced due to the presence of other electrons in between them.

In an atom, electrons are arranged in different energy levels or shells. Electrons in the inner shells provide a "shielding" effect for the electrons in the outer shells from the full charge of the nucleus. This is because the inner electrons repel the outer electrons, reducing the net attractive force from the positively charged nucleus.

The shielding constant is important because it helps us understand and predict various atomic and molecular properties, such as ionization energy, atomic radius, and reactivity. For example, in multi-electron atoms, the outermost electrons feel a reduced effective nuclear charge due to shielding, which can influence how easily those electrons can be removed or how they interact with other atoms and molecules.