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# Group trend for ionization energy

Video transcript

Ionization energy
refers to the energy that's required to remove an
electron from a neutral atom. So if we look down here, this
A represents a neutral atom, meaning equal numbers of
protons and electrons. And since the positively
charged nucleus is going to attract those
negatively charged electrons, it's going to take energy
to pull an electron away from that attractive
force of the nucleus. And so that's your
ionization energy. If you take away an
electron, you no longer have equal numbers of
protons and electrons. You'd have one more proton
than you do electrons. And so you get a
plus 1 charge here. So you form an ion. And so ionization energy is
always going to be positive. So it always takes energy
to pull an electron away. So positive value for
ionization energy. And our units are
kilojoules per mole. And in this video,
we're only going to be talking about the
first ionization energy. So IE 1, like that. Let's look at some actual
ionization energies for elements in group one. And so we can see here
some elements in group one. And so for hydrogen, it
would take 1,312 kilojoules per mole of energy to pull an
electron away from hydrogen. For lithium, it would take
about 520 kilojoules per mole to take an electron away. And we can see as we go down
here, the number decreases. So sodium would be 496. Potassium would be 419. So there's a clear trend. As we go down a group
in the periodic table, there is a definite decrease
in the ionization energy. So it must be easier to
pull an electron away. So let's see if we can
figure out the reason why. And we're going to study in
detail here these two elements. So hydrogen and lithium. So let's go ahead and look
at these diagrams here. We're going to fill them in
for hydrogen and lithium. And so for our first diagram,
we will put hydrogen. So hydrogen has an
atomic number of one. So there's one proton
in the nucleus. So a plus 1 charge
in the nucleus. And in a neutral atom,
there's one electron. So we can go ahead and draw in
hydrogen's one electron right here, like that. The electron configuration
would be 1s1. So that one electron is in an
s orbital in the first energy level. So this negatively
charged electron feels an attraction for this
positively charged nucleus. And so to pull it away,
you must add energy. So if you add 1,312
kilojoules per mole of energy, you can pull that electron away. And if you do
that, you'd be left with just a positive one charge
in the nucleus and no electrons around it. And so you no longer
have a neutral atom. You have an ion. You have H plus, because you
have a positive charge of one in the nucleus and
zero electrons. So H plus. So that's the concept of
ionization energy here. Let's look at lithium. So down here,
we'll draw lithium. Lithium has an atomic
number of three, so three protons in the nucleus. And in a neutral
atom, three electrons. So the electron
configuration is 1s2, 2s1. So there are two electrons
in the first energy level and they're in an s orbital. So I'm going to go ahead
and draw those in here. So these two
electrons I just drew represent the two electrons
in the first energy level. In the second energy level,
there's one more electron. So I'm going to put that
electron down here like that. So for lithium, if we were
to take an electron away, the one that's most
likely to leave would be this outermost
electron here, the one in the 2s orbital. So if you apply 520
kilojoules per mole of energy, you can pull away that electron. And so if you did
that, you'd be left with a plus 3 charge
in the nucleus. And you would still have your
electrons in the 1s orbital, so I'm going to go ahead
and draw those in there, but you've taken away
that outer electron. And so therefore, you'd
have a lithium cation here. You'd have Li plus
1, because you have three positive
charges in the nucleus and only two electrons now. So 3 minus 2 gives you plus 1. The electron configuration
for the lithium cation would therefore be 1s2
because we pulled away that outer electron
in the 2s orbital. So this is the picture
for the ionization of hydrogen and lithium. And we're going to examine
some of the factors that affect the ionization energy. And so first we'll talk
about nuclear charge. So let me go ahead and
write nuclear charge here. So the idea of nuclear charge
is the more positive charges you have in your nucleus, the
more of an attractive force the electron would feel. And so therefore,
the harder it would be to pull that electron away. So in general, you could think
about increased nuclear charge. That would want to increase
the ionization energy. Because again, there's a
greater attractive force for the electrons. So let's look at
these two situations, and let's think
about hydrogen first. So hydrogen has a plus
1 charge in the nucleus. And this one electron here
would be pulled to the nucleus by that positive charge. If we look at lithium,
plus 3 in the nucleus. So that's a greater
nuclear charge. So just thinking about
nuclear charge alone, you would think, oh,
well this electron might be pulled in even
more than with hydrogen, because plus 3 is
greater than plus 1. And so just thinking
about nuclear charge for these two things, that would
seem to indicate that lithium's outer electron would have
a greater attractive force for the nucleus. So therefore, you might think
it might take more energy to pull that electron away. So just thinking
about nuclear charge, we might think an increase
in the ionization energy. Next, let's talk about
electron shielding. So electron shielding,
or you could also call it electronic screening. So the idea of
electron shielding is the inner shell
electrons are going to shield the outer electrons
from the positive charge of the nucleus. And let's look at lithium
for an example of that. So we have these two
inner shell electrons are going to repel the
outer shell electrons. So this electron
in blue is going to repel this electron in
green, and this electron in blue is going to repel this
electron in green. And so they're going to
shield that outer electron in green from that positive 3
charge, because electrons repel other electrons. Like charges repel
other like charges. And so that's the idea of
electron shielding or electron screening. And so thinking about just
this factor, for lithium, these two inner
shell electrons are going to shield that
outer shell electron. There's going to be a force
in the opposite direction, if you will. And so that means that
it would be easier to take that outer electron
away due to the repulsive force of those electrons. And so if we just think about
electron shielding or electron screening by itself,
it would be easier to take away lithium's
outer electron due to the shielding effect. And so therefore, you
would need less energy. So a decrease in the
ionization energy if we're just thinking
about this factor. Now, nuclear charge and electron
shielding go hand in hand. And one way to
relate those would be to think about what's called
the "effective nuclear charge." So I'm going to
go ahead and write the effective nuclear
charge, so Z eff, is equal to the
nuclear charge, which is Z, minus the effect of
the shielding electrons. And so this is one
way to think about it. This is a very simplistic
way of doing the math here. So let's look at hydrogen
first and calculate the effective nuclear charge
that this electron experiences. Well, there's a plus 1
charge in the nucleus. So that's the nuclear
charge, Z. And there are zero shielding electrons. So 1 minus 0 is,
of course, plus 1. So this outer
electron experiences an effective nuclear
charge of plus 1. For lithium, there are three
protons in the nucleus. So Z would be plus 3. And there are two
shielding electrons, these two inner
shell electrons here. So it would be plus 3 minus 2. So the effective nuclear
charge would be a plus 1. So if you think about it,
the effective nuclear charge that hydrogen's electron
feels is about the same as lithium's outer electron,
because they both have an effective nuclear
charge of plus 1. So the fact that lithium
has this electron shielding, or electron screening,
that kind of cancels out this effect of the
nuclear charge. And so these two things
kind of cancel out. Now, of course, this is a
very, very simplistic way of calculating the
effect of nuclear charge. In reality, for lithium, if you
do it the more complicated way, you actually get a value
of approximately 1.3. So we can say that lithium's
effective nuclear charge is close to positive
1, even though it's a little bit more accurate
to say it's around 1.3. And so for our purposes, the
electron shielding for lithium cancels out that
increased nuclear charge. And so we have to look
at the last factor to understand this trend. And the last factor
is the distance of that outer electron
from the nucleus. So let's think about that. So for hydrogen, this electron
is pretty close to the nucleus. And the closer it is, the
more of an attractive force it has for the nucleus. So once again, in
physics, Coulomb's law, it's distance dependent. The closer you are, the
more of an attractive force you will feel. So that electron feels a
very strong attractive force, so it's hard to pull
an electron away. For lithium, this
outer shell electron is, on average, a
further distance away from the nucleus, and so
therefore, doesn't have as much of an attractive pull
towards the nucleus. There's not as great
of an attractive force, so it's easier to pull
that outer electron away. If it's easier to pull
that outer electron away, that, of course, would mean
a decrease in the ionization energy. So because of
distance, we can say that it's easier to pull
that outer electron away from lithium because it's
further away from the nucleus. And so thinking about all
three factors at once, the nuclear charge and the
electronic shielding effect sort of cancel each other out. And so we can just think
about the distance factor to explain the trend
that we see in groups for ionization energy.