for the periodic table of elements

for dimensions like ionization energy,

atomic and ionic radii, electron affinity,

and electro negativity.

And to do so, we're going to start with

a very fundamental idea in chemistry or physics,

and that's Coulomb's Law.

And for our point of view, we can view Coulomb's Law

as saying that the magnitude of the force

between two charged particles is going to be

proportional, that just means proportional right there,

is going to be proportional to the charge

on the first particle times the charge

on the second particle, divided by the distance

between those two particles, squared.

When we're thinking about it in context

of the periodic table of elements and various atoms,

you can view q1 as the effective positive charge

from the protons in the nucleus of an atom.

You can view q2 as the charge of an electron.

Now any given electron is going to have

the same negative charge, but as we try to understand

trends in the period table of elements,

it's really the outer most shell electrons,

the valence electrons, that are most interesting.

Those are the ones that describe the reactivity.

And so when we think about the distance

between the two charges we're mainly going to be

thinking about the distance between the nucleus

and those outer most valence electrons.

Now we can view this effective charge,

I'll call it z-effective, as being equal to the difference

between the charge in the nucleus,

so you can just view this as the atomic number,

atomic number or the number of protons

that a given element or an atom of that element has,

and the difference between that and what is often known as

S, or how much shielding there is.

Now there is complicated models for that,

but for an introductory chemistry class,

this is often approximated by the number of core electrons.

Remember, we really want to think about

what's going on with the valence electrons.

And so if you imagine a nucleus here,

do that orange color, that has protons in it.

And so you have core electrons.

Let's say these are the core electrons in the first shell,

and then you have some core electrons in the second shell.

And let's say the valence electrons are in the third shell.

So let's say these are some valence electrons here,

they're blurred around, they're in these orbitals.

Those valence electrons, which have a negative charge,

are going to be attracted to the positive charge

of the nucleus but they're also going to be

repulsed by all these core electrons

that are in between them.

And so that's why an approximation

of the effective charge that these valence electrons

might experience is going to be the charge

of the nucleus minus, and this is an approximation,

the number of core electrons that you have.

So if we use that roughly as a way to think about

z-effective, what do you think are going to be

the trends in the periodic table of elements?

What would be the effective charge

for the Group I elements over here?

Well, Hydrogen has no core electrons

and it has an atomic number of 1.

So 1 minus 0 is going to have

an effective charge of roughly 1.

Lithium atomic number of 3, minus 2 core electrons

that are in 1-S, so once again you're going to have

3 minus 2, effective charge of 1.

So roughly speaking, all of these Group I

elements have an effective charge of 1.

What if you were to go to the halogens?

What's the effective charge there?

Well if you look at Flourine, atomic number of 9,

has 2 core electrons in the first shell,

so has an effective charge of 7.

Chlorine actually has an effective charge of 7

for the same reason.

Atomic number of 17, but 10 core electrons.

If you go even further to the right,

to the noble gases, you see that Helium

is going to have an effective charge of 2,

atomic number of 2 minus 0 core electrons.

But then when you get to Neon,

you have an atomic number of 10,

and then minus only 2 core electrons.

And you'll see as you go down these noble gases,

other than Helium, they have an effective charge of 8.

And so the general trend is, your effective charge is low

at the left, effective charge low for Group I,

and then when you go to the right of the periodic table,

you have a z-effective, is going to be high.

So within a given period, or within a given row

in the periodic table of elements,

your outer electrons, your valence electrons,

are in the same shell.

But the effective charge is increasing

as you go from left to right.

So this q1 right over here is going to be increasing.

So what is that going to do to the radius of the atom?

Well, Coulomb's Law will say that the magnitude

of the attractive force between those opposite charges

is going to be stronger.

And so even though you're adding electrons

as you go from left to right within a row,

within a period, the atoms in general

are actually going to get smaller.

Let me write it this way.

So as you go from left to right, generally speaking,

radius decreases.

Now what's the trend within a column?

Well one way to think about it is,

as you go down a column, as you go down a Group,

you're filling shells that are further out.

And so you'd expect radius to increase

as you go down a column, or down a Group.

Or you could say radius decreases as you go up a group.

So radius decreases.

So overall what's the trend

in the periodic table of elements?

Well radius is going to decrease as you go

up and to the right.

And so you could draw an arrow something like this.

And it is indeed the case that by most measures,

Helium is considered to be the smallest atom,

a neutral Helium atom.

And Francium is considered to be the largest atom.

So could we use this to think about

other trends in the periodic table of elements?

What about, for example, ionization energy?

Just as a reminder, the first ionization energy

is the minimum energy required

to remove that first electron

from a neutral version of that element.

And since it's the minimum energy,

it's going to be one of those outer most electrons.

It's going to be one of the valence electrons.

And so what's going to drive that?

Well you can imagine the ionization energy

is going to be high in cases where

the Coulomb forces are high.

And what are the situations where

the Coulomb forces are high?

Well this is going to be a situation

where you have a high effective charge

and where you have a low radius.

Low radius makes the Coulomb forces high.

And effective charge makes the Coulomb forces high.

So where is that true?

So you have the lowest radii at the top right

and you have the highest effective charge at the right.

So you would expect the highest ionization energies

to occur in the top right.

So high ionization energy.

And that actually makes intuitive sense.

These noble gases are very stable.

They don't want to release an electron.

So it's going to take a lot of energy

to take one of those electrons away.

Fluorine or Chlorine, they're so close

to completing a shell, the last thing they want to do

is lose an electron.

So once again, it takes a lot of energy

to take that first electron away.

On the other hand, if you go to something

like Francium, it has one valence electron.

And that valence electron is pretty far from the nucleus.

And there's a low effective charge

despite all the protons because there's so much

shielding from all those core electrons.

So it's not surprising that it doesn't take

a ton of energy to remove

that first electron from Francium.

Now another trend that we can think about,

which is in some ways the opposite,

is electron affinity.

Ionization energy is talking about the energy

it takes to remove an electron.

Electron affinity thinks about how much energy

is released if we add an electron

to a neutral version of a given element.

So high electron affinity elements,

these are the ones that really want electrons.

So they should have a high Coulomb force

between their nucleus and the outer most electrons.

And so that means they should have

a high effective z, and that also means

that they should have a low r.

So one way to think about it, you're going to have

a similar trend with the one difference that

the noble gases don't like gaining or losing electrons.

But we do know that the Flourines and the Chlorines

of the world can be become more stable

if the gain an electron.

They can actually release energy.

So you actually have high electron affinities

for the top right, especially the Halogens.

And you have low electron affinities

at the bottom left.

Now there's one little quirk in chemistry conventions,

people will generally say that Fluorine and Chlorine

and the things in the top right that aren't noble gases,

have a high electron affinity.

And it is the case that energy is released

when you add an electron to a neutral version of them.

It just happens to be that the convention,

and this can get a little confusing,

is that when you release energy you have

a negative electron affinity.

But generally speaking, when they say

a high electron affinity, this thing's going to release

more energy when it's able to grab an electron.

Now a notion that is related to electron affinity

is electro negativity.

And the difference between the two can sometimes

be a little bit confusing.

Electro negativity is all about when

an atom shares a pair of electrons with another atom,

how likely is it to attract that pair to itself

versus for the pair to be attracted away

from it to the other one?

And so you can imagine it correlates very strongly

with electron affinity.

Things that release energy when they're able to be

ionized to grab an electron, if they form a bond

and they're sharing a pair of electrons,

they are more likely to hog those electrons.

Electron affinity is easier to measure.

You can actually see when this element's in a gaseous state

if you add electrons how much energy is released,

it's normally measured in kilojoules per mole

of the atom in question.

While electro negativity isn't as clear cut

on how to measure it, but it can be a useful concept

in future videos as we think about

different atoms sharing pairs of electrons

and where do the electrons spend most of their time.

So I'll leave you there.

We started with Coulomb forces and we were able to

intuit a whole bunch of trends just thinking about

Coulomb's Law and the periodic table of elements.