Today’s video is about shielding and effective nuclear charge. Shielding and effective nuclear charge are in a sense two sides of the same coin.
It gives us a model to understand how the behavior of atoms derives from the interplay of positive and negative particles in the atom. And we call that behavior atomic properties.
More specifically shielding and effective nuclear charge refer to how the interplay of positive and negative affect the valence electron shell since that is primarily where chemistry occurs.
There are two forces in the atom that result in the chemistry we experience.
One is the negative electron and positive proton exerting an attractive force on each other. The other is the repulsive force exerted by electrons.
With the exception of hydrogen, all atoms have more than one each of electrons and protons.
So in this video we will look at the collective result of attractions and repulsions among multiple protons and electrons within a single atom, which are referred to as shielding and effective nuclear charge;
and also, how do these forces affect atomic properties and the periodic trends of properties.
Let’s begin by looking at second period elements starting with lithium, the first element in period 2.
For this presentation, protons are blue and electrons are violet, and the model of the atom we will use throughout this video shows concentric circles representing the principle quantum number n, which is also called the electron shell.
The word shell is synonymous with principle quantum number. Lithium has three protons in its nucleus.
The electron configuration shows one valence electron, and two inner electrons, also called ‘core’ electrons.
How electrons are arranged relative to each other is an important part of understanding shielding and effective nuclear charge as we shall see throughout this video.
We will represent the attractive force of each proton with an inward pointing blue arrow.
What is next is essential to understanding shielding and effective nuclear charge, which is the repelling effect that core electrons have on valence electrons.
Here, the repulsive force is represented by outward pointing violet arrows, and the valence electrons experience less attraction by the nucleus because of the repulsions of core electrons.
As we know however, electrons are not stationary.
They are in constant motion creating a cloud of negative charge which we call the orbital.
So, there is not a single direction of repulsion from single point particles, the repulsion from the cloud occurs in all directions.
So the question we can now approach is, how much attractive force does the valence electron feel from the nucleus?
In this model each repelling arrow has the effect of opposing the attractive force of one proton.
We can show the effect of this opposition by cancelling the attractive force of two protons due to the repelling force of two core electrons.
The net effect of these opposing forces is that the valence electron feels only the attractive force of a single proton.
And since chemistry occurs at the valence level, this result of the interplay of positive and negative, that is, the amount of attractive force felt by the valence electron has large consequences for the atom’s properties, which we will go further into throughout this video.
So we are now in a position to more specifically define shielding and effective nuclear charge. Shielding…
Note that the total nuclear charge is denoted by an upper case Z.  Effective nuclear charge, abbreviated Z–sub–e-f-f, and which we will refer to as “ZEFF,”
zeff is simply an accounting of the amount of attraction felt by the valence electrons.
It is represented in this equation where S is a somewhat estimated number because it can be represented by more than one possible calculation.
However, two factors that influence the value of S should be noted:
One is that because valence electrons move in orbitals that can penetrate the orbitals of core electrons, and this momentary position of being below core electrons results momentarily in reduced repulsions by core electrons.
That results in lowering S. However, valence electrons also repel each other, resulting in a slight increase in S.
Due to these considerations it is reasonable to approximate S as simply the number of core electrons.
Zeff is approximated by subtracting the amount of protons by the amount of core electrons, just as we removed the amount of attracting arrows equal to the amount of repelling arrows.
So for lithium Zeff is 1, which is 3 protons 2 core electrons.
The full attractive force of the nucleus is reduced by the repulsions of electrons.
And the effective nuclear charge, Zeff,
is often represented by a number with a plus sign since it shows the net attraction of the nucleus.
In the remainder of the video, we will look at….
Let’s begin by looking at the next element in period 2, beryllium.
Beryllium has a nuclear charge of 4+, one more than lithium.
Both elements have two core electrons in 1s.
Lithium has one valence electron while beryllium has two valence electrons.
So the amount of shielding in beryllium remains the same as in lithium.
That is, two core electrons, but beryllium has four protons exerting an attractive force.
The two shielding electrons cancel two attracting arrows, and so now we have an effective nuclear charge, or Zeff, of 2.
Four protons minus two core electrons, compared to a Zeff of 1 for lithium.
Let’s skip down a bit in period 2. Let’s go to fluorine. Fluorine has nine protons.
Again we wee that there are two core electrons, so repulsions have not changed in period 2.
. However, with nine protons, two core electrons cancel two positive charges, and we have an effective nuclear charge of 7.
With understanding this we can get a good look at the property of atomic size.
You may notice that the atoms get smaller going from left to right across the second period. Why would that be the case?
Why do atoms show periodicity in size?
We can see that the amount of protons increases across the period, and the added electrons go to the same shell –the same principle energy level.
But core electrons remain constant, and so the attractive force of the nucleus increases which is shown by the value of Zeff.
Each increase in attractive force pulls the electrons further inward, reducing the size of the atom.
Atoms get smaller going across a period from left to right.
This explains the periodicity, the property trend, of atomic size....
Now let’s take a look at what happens to shielding and effective nuclear charge when we go to the next period.
Let’s compare the last element in period 2, neon, to the first element in period 3, sodium.
Neon has ten protons and two core electrons giving it an effective nuclear charge of 8, and a small radius.
When going to the next element, sodium, several changes occur.
. Sodium’s single valence electron is in a higher energy shell, it is in n = 3.
It is at a higher energy than any other electron so its orbital is large and its average distance from the nucleus is greater.
What is most important about this is that it puts neon’s eight valence electrons in the core.
So the amount of shielding electrons suddenly increases from two to ten.
This is also a sudden increase in repulsions, pushing the valence electron even further out, and reducing Zeff to 1, so a dramatic decrease in the attracting effect of the nucleus.
The result is a much larger radius compared to neon.
Now let’s take a look at atoms residing in the same group.
Let’s scale up sodium to compare to lithium, going down the alkali metals.
We will compare shielding, Zeff, and resulting properties. Lithium has three positive charges, sodium has eleven.
Lithium has two shielding electrons but sodium has ten due to the added valence shell.
And they both have one valence electron.
But sodium’s valence electron is in that higher principle energy level
and it is being repelled by ten core electrons instead of two, so that single valence electron is further from the nucleus and the radius of sodium is larger.
Interestingly the effective nuclear charge for both lithium and sodium is 1.
Three protons versus eleven, and two core electrons versus ten, gives both a Zeff of 1.
The importance of that we will discuss further in a moment.
Let’s put these in a column so we can add potassium, the next alkali metal.
And also look at periodic patterns and properties, otherwise known as periodicity.
Potassium is in the fourth period, and you can see that potassium adds another principle energy level for its valence electron.
This puts the eight valence electrons from argon into the core,
so shielding increases and there is suddenly a great deal more repulsion.
For potassium, like the other alkali metals, Zeff is also 1.
We can see the resulting pattern in size.
Going down any group, energy levels are added & so:
Here, Zeff has little impact on size from one element to the next.
The pattern for atomic size going down a group is that atoms get larger.
The two patterns of atomic size, decreasing across a period and increasing down a group at first might seem contradictory,
since in both cases equal amounts of protons and electrons are being added, but they have the opposite effect.
Because of shielding and effective nuclear charge:
Atoms lose and gain electrons in the course of a chemical reaction.
Because electrons are attracted to the nucleus energy is required to remove them. The unit for IE is kilojoules per mole of atoms.
In other words how much energy does it take to remove a mole of electrons from a mole of atoms?
Normally, it is valence electrons that are removed since they have the least attraction to the nucleus.
So if we take a look at what’s happening across the second period
we can see that the valence electrons get closer to the nucleus,
which means the nucleus has a tighter hold on them.
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The last thing we will look at is the group trend for ionization energy using the first three alkali metals as an example.
We know that with effective nuclear charge: [above, yellow bullets]
So, similar to the size trend, changes in electrons and protons result in opposite trends in ionization energy due to the location of added electrons.
One last question remains, at least for this video.
We have focused only on main group elements, while ignoring what happens when you go through the transition metals.
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Again, depending on the location within the d orbital where a new electron is added we can get a variety of changes in stability.
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