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Chapter 3.5 Periodic Variations

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the topic of this video is periodic

variations in element properties

and the learning objective is shown on

your screen to

to jump into the discussion of atomic

size it's helpful to first talk about

the definition of covalent radius

the reason that we are using covalent

radius is that's just one way to

discuss atomic size

so the covalent radius is one-half the

distance between the nuclei

of two identical atoms when they are

joined by

a covalent bond and some examples

of of covalent radius are

shown in this figure on your on top of your

your

screen here that i'm circling in red and

what we have are different halogen molecules

molecules

such as f2

for molecular fluorine but we also have

molecular examples of the other halogens

here as well

now the covalent radius is then going to be

the half the distance between the nuclei here

here

in this covalent bond so half the

distance for

molecular fluorine is 64 picometers but

you can see as we

as we move along from from chlorine to chlorine

chlorine

bromine and iodine the atomic

size or the covalent radius is increasing

increasing

so let's drop down here to look at the

periodic table

that it has some nice convenient relative

relative

spheres drawn for each um atom so we can see

see

or for each element uh that sort of

helps us to to see

general size trends let's

go ahead and focus again in the halogen box

and here just as we have discussed

looking at the actual molecules of

of these particular halogens halogens we

can see here that indeed as we go

down this period uh the the size gets bigger

bigger

the uh general explanation general

explanation for this

is that the as we drop down from let's say

say

fluorine to chlorine we are also

increasing our principal quantum number

so instead of being in the 2p we are in

the 3p

subshell and what that means is at the

higher principle quantum number value

we are at a higher relative energy

and we're also uh going to be at a larger

larger

relative size so so that's pretty much

the the main trend here is that as we go

down across any period in the periodic table

table

um the size is going to increase

conversely you could say going

up in any period the size will decrease

and i'll draw out some general

trends in a second now

the it's a little bit different now to

consider what happens when we move

from left to right across this

particular periodic table

if we look for example at

the 2p main group block here

what you'll see is that boron is

actually large

relative to carbon and the size keeps

going down and down as we go further

from left to right okay so

going from left to right and indeed

fluorine is one of the smallest

elements so what can explain this because

because

as we add more electrons the size is

decreasing and that can be

a little counterintuitive you're adding

more electrons why

is it decreasing in size and this has to do

with um uh this interplay between

the charge of the nucleus um

so we'll write that the nucleus is has

this positive charge at the center

and um we can also think about um

even though we've done a good deal of

talking about

um electrons as waves i'm going to for

this example

just draw it as a particle uh because

it's kind of

um convenient to do so so there's

clearly going to be

a force of attraction here uh that i'm

drawing in green

between the negatively charged electron

and the positively charged

nucleus for the case of hydrogen atom

where there is only one electron and

only one proton this is a

straightforward case to calculate

what is called the nuclear charge okay

so nuclear charge is

designated as capital z

okay and that is literally just the

number of

protons in a nucleus now the case

becomes a little more complicated as we

might add more protons to the nucleus

that would increase the nuclear charge but

but

becomes even more complicated if we add

now into any given subshell another electron

electron

because while the a second electron will indeed

indeed

feel a force of attraction um to the

positively charged nucleus the electrons

that now are sort of in closer proximity

in space

are now going to repel one another

because they are the same negative charge

charge

so what happens in cases where we have

more than one

um electron we actually need to

designate what's called z sub f

e f f and this is the effective

nuclear charge so this means that

because of this um

right the the electron electron

repulsion happening

that no electron actually feels the full um

pull of the nucleus and so we can calculate

calculate

z effective or uh the effective nuclear charge

charge

by taking the nuclear charge minus

something that we call

shielding and we don't need to use any

particular values here although it can be

quantified but essentially what this

means is when we add

a given atom that the electrons are not

necessarily going to feel the full force

of being attracted to the

to the nucleus now um one final thing

is that when we think about shielding

not all

electrons shield to the same extent okay so

um core electrons

are good at

shielding okay

so the so core electrons will provide a

lot of shielding

to subsequent electrons to the valence

electrons but

valence electrons do not shield

each other well

so this is really the most important one

to keep in mind the second one here

uh to explain why the atomic

size or the covalent radius is going to

be decreasing from left right

valence electrons do not shield each

other well so what that means is

i'm going to jump back up to this figure

if we compare starting from boron

to going to carbon for example here

boron to carbon

carbon has one more electron right that

is a 2p2

now it's 2s22p2 rather than 2s2 2p1 for boron

boron

but carbon also has one more proton than boron

boron

and even though those electrons now

carbon has more electrons in the p subshell

subshell

so they should be repelling each other

you'd think maybe that would be bigger

but because the valence electrons in

this 2p subshell don't shield each other

very well

the the second electron that

carbon has in the 2p subshell actually

feels a very strong

um effective nuclear charge because

there is minimal shielding

from two p electrons okay so

essentially it has to do deal with the

fact that

the size decreases from the left to the

right across the periodic table because

valence electrons do not shield each

other all that well so the effective

nuclear charge is high

and that helps contract the the atomic size

size

to summarize the the the trend in size

here i'll just

leave you with this um one of the ways

that i think is very straightforward to

remember the trends in atomic size

is that size decreases up and to the

right on the periodic table

if you just remember this sort of arcing

shape of going up and to the right and

remember that this is

the trend for size decreasing

that might be one way to help you remember

remember

this trend next i'm going to quickly discuss

discuss

the variation in ionic radii

variation in ionic

radii so the um the general rule is that

if something becomes uh loses electrons

so let's take a look at

aluminum neutral atom for a second which

has a

covalent radius of 118 picometers

if we um lose three

electrons okay minus three electrons

what we'll do

is end up with the aluminum

three plus cation and i intentionally

drew this

uh smaller because this actually has

a an ionic radius of

68 picometers so it

shrunk drastically and that's because as

you remove electrons there's

less and less electron electron

repulsion and

um so those electrons that are remaining

feel a higher degree of of effective

nuclear charge and so

they contract on the other hand

it's the opposite case for when

something let's say sulfur for example

takes electrons so here we are adding

two electrons to sulfur

sulfur neutral atom is 104 picometers

and when it took two electrons it

ballooned up

to sulfur two minus or sulfide

and this is now 170 picometers so

substantially larger

and again this is because now we're

adding more electrons

into the valence shell of sulfur there's

more electron electron repulsion so

relative to the neutral atom

it's going to be a larger size the the um

the anion here sulfide now

there's one special case well there's a

special term

for ions that have the same electron configuration

configuration

so let's look at a couple of different

ions let's look at o2 minus

f minus sodium plus

and magnesium two plus all of which

share the electron configuration 1s2

2s2 2p6

and you might also just recognize that

noble gas configuration okay so this

could just be

summarized as this

so all of these ions are said to be

because they share the same electron

configuration okay

now if you're good if you need to

compare the sizes of isoelectronic ions

there's a few ways you can do it

one you can look at the charge right so

you can say if they're isoelectronic i

know that they have the same number of

valence electrons um

uh they essentially have the exact same

electron configuration

so in order to get that exact same

electron configuration

the the ions that have um negative

charges and specifically

um uh the higher the negative charge the

bigger the uh

the ion should be because it had to ex

expand to accommodate those extra electrons

electrons

so um what we would say here is that we

would predict o2 minus

is going to be bigger than um f minus

now for the uh oh i forgot to put a plus

on the magnesium two plus over there

um so now if we wanted to think about

what's the size of the cations relative

to here well in order to get to the

uh with o2 minus and f minus they had to

lose electrons

and the more electrons that an atom

loses the smaller it gets so we would

predict here that

sodium plus would be even smaller yet

and the smallest would be

magnesium two plus now that's one way to

do it by evaluating charges

um another way to do it is just to look

at the

the nuclear charge and

if you just compare the nucle the

general rule of thumb here is that

the greater

in a series of

iso electronic

ions and

atoms up next we can

think about trends in ionization energy ionization

amount of energy

required to

release an [Music]

[Music]

electron from

an atom in the gas phase

an example of this would be sodium gas

which is the neutral atom going to

sodium cation

gas plus electron um

and so when we are talking about the

first ionization energy you'll often see

it referred to as capital i capital e

sub 1.

so here are some trends across

so it's ionization energy on the y axis

and then on the x axis we have atomic

number and then it's also broken down

into different periods

so you'll see that there is some

periodicity here um

we have some jumps in first ionization

energy that go back down go back up go

back down

from from as we move across each period

um so some uh trends that i want to talk

about uh

first are that the ionization energy

within a group

tends to go down so if you go down in

the periodic table

ionization energy will also go down that

is it's easier to remove

an outermost electron if we move from the

the

left to the right across a period what

we see is that ionization energy

typically is increasing

and so the effective nuclear charge

is higher uh for those extra electrons

that we're adding as we go from left to

right so that's one of the reasons why

the size decreases but also

it would require more energy to remove

that electron so those are two

general trends in first ionization

energy i do want to point out

um you know one of the uh uh anomalies

here or seemingly anomalies

uh so this is kind of circled so much

here so let me try to click

clear this up a little bit so when we

jump up from let's say

we could look at beryllium to boron and

we can also look at nitrogen to oxygen

i'm going to look at nitrogen

to oxygen that that slight decrease

that's because if we look at the

orbital diagram uh

let's say nitrogen so nitrogen is

i'm stuck here 2p3

so the um energy well not the energy

diagram but the orbital

orbital diagram looks something like

this so we have

one two one two and then we have a

completely half filled

okay so now the the difference between

that and oxygen is oxygens 1

2 2 s 2 2 p 4

so we draw the exact same diagram here

and we have two electrons here two

electrons there and now we're going to

add one

two three and we're going to actually

pair up the electrons here

because that's our only choice we've

already distributed them equally

into the 2p subshell and now we have to

pair them

that pairing process electron pairing

actually is slightly

unfavorable okay so there is some what's

called uh uh

some repulsion even within this um particular

particular

pairing here so what that means is that

that paired electron

the paired electron

to remove

than the corresponding non-paired electron

electron

up here in nitrogen so because that

paired electron is easier to remove an

oxygen that's why we see this

um little decrease here in that first

ionization energy it becomes slightly

easier to easier to remove that outer

most electron and oxygen but then the

trend resumes again with fluorine

finally we'll talk about electron affinity

which is again a negative ion

so some of the atoms that have the highest

highest

electron affinity that is they have the

most amount of energy released when they

accept an electron here

high electron

affinity on the other end of the

scale we have things um

such as beryllium okay over here with

plus 240

which is a calculated value um

and this has low electron infinity it

does not

okay but the general trend here uh just

i just want to point those two out is

sort of

two extreme examples the general trend

is that moving from left to right across

the period the electron affinity is

from the lower part of a group to the

upper part of a group

the electron affinity also increases

generally speaking so what this means is

and of course there are exceptions all

over this

particular periodic table but the

overall trend is

up and to the right electron affinity is increasing

increasing

okay that's the general rule of thumb

electron infinity is

increasing and uh the reason that i

mentioned up into the right electron

affinity is increasing

is because that kind of tracks nicely if

we think about

earlier when i was talking about size

where up and to the right size is decreasing

decreasing

okay effective nuclear charge is increasing

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