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## Periodic table trends

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# First and second ionization energy

## Video transcript

In the previous videos
we've talked about only the first ionization energy. In this video, we're
going to compare the first and the second
ionization energies, and we're going to use
lithium as our example. So in the previous
video, we already know that lithium has
an atomic number of 3, so there are three
protons in the nucleus. In a neutral atom of lithium,
the number of electrons equals the number of
protons, and so we know there are three
electrons in lithium here. The electron
configuration is 1s2 2s1. So we have two electrons
in the 1s orbital so we can go ahead
and put those two electrons in the 1s
orbital like that. And then we have
one more electron, and that electron's going to go
into the 2s orbital like this. And so that would be
a very simple picture of the neutral lithium atom. If we apply enough
energy, we can actually pull away this
outer electron here. So we can pull
away that electron, and we call this the
first ionization energy. And to pull away
that electron takes approximately 520
kilojoules per mole. And so once we've pulled
that electron away, we no longer have a neutral
lithium atom, right? We would have a lithium
ion because we would still have three positive
charges in the nucleus, but we have only two
negative charges now. We only have two electrons
because we pulled one away. So 3 minus 2 gives us plus 1. So this is the
lithium plus 1 cation. And the electron
configuration would just be 1s2 because we lost the
electron in the 2s orbital. And so we could keep going. We could apply some more energy
and pull away another electron. So let's say that we pull
away this electron this time. OK, so we're taking a
second electron away, and so we wouldn't call
this ionization energy 1. We would therefore call
this ionization energy 2 because this is to take
away the second electron. And this value turns out to be
approximately 7,298 kilojoules per mole. And so if we take away that
second electron, once again we still have three positive
charges in the nucleus, but we have only one
negative charge now. There's only one electron
so this is no longer the lithium plus 1 cation. This is the lithium plus
2 cation because 3 minus 1 is plus 2. So this is lithium plus 2 here,
and the electron configuration would be only one electron
in a 1s orbital, so 1s1. So we can see that there
is a big difference between the first
ionization energy and the second ionization
energy, so 520 versus 7,298. So let's see if we can
explain the reasoning for this extremely large
difference in ionization energies. And we're going to use the
three factors that we've talked about in the
previous videos. So the first factor we
discussed was nuclear charge, which refers to the number
of protons in the nucleus. So if we look at the
neutral lithium atom, three positive charges
in the nucleus. That positive charge
is what's going to attract this electron
in magenta here. And if we look at
the lithium plus 1 cation, similar situation. We still have three
protons in the nucleus, and so that positive
charge is what's going to be attracting
this electron as well. And so because of the
same number of protons, we have to think more about
effective nuclear charge, as opposed to how many protons
there are in the nucleus. And before we do that,
we have to consider the effect of
electron shielding. So let's talk about
electron shielding next. So electron shielding, also
called electron screening, so electron shielding
slash screening. So when we think about
electron shielding, we're thinking about the
inner orbital electrons here. So going back to the
neutral lithium atom, these two inner shell
electrons right here are going to repel this
outer shell electron. So this one is going to
repel this one as well. And so we can think about it
as they screen the electron in magenta from feeling the full
force of the positive 3 charge in the nucleus because
electrons repel other electrons. And so the way to calculate
the effect of nuclear charge-- so we've done this in
the previous videos as well-- the simple
way of calculating effective nuclear charge is
take the number of protons, so plus 3, and from
that you subtract the number of
shielding electrons. So in this case, it would
be these two electrons in the 1s orbital. So 3 minus 2 gives us an
effective nuclear charge of plus 1. And so the electron
in magenta isn't feeling a nuclear
charge of plus 3. It's really only feeling an
effective nuclear charge close to positive 1 because the actual
value is approximately 1.3 when you do the more
complicated calculations. And so the effect of
electron shielding is to decrease the
overall nuclear charge that this electron
magenta feels. And so when we move over
here to this electron, so I'm talking about
this electron in magenta for the lithium
plus 1 cation, it's not the same situation, right? There's not much
electron shielding. This electron over here
might repel it a little bit, but there are no
inner shell electrons repelling this
electron in magenta. And because of that,
the electron in magenta is going to feel this
positive 3 charge, much more of the full positive
3 charge of the nucleus. And so therefore,
there's going to be a much greater
attractive force holding this electron in
magenta to this nucleus. And therefore, you have
to apply more energy to pull that electron away. So the effect of
electron shielding tells you the second
electron is much harder to remove than the
first, and so we see a large increase
in ionization energy from the first ionization
energy to the second ionization energy. The last factor that we
discussed was distance, so the distance of those
electrons in magenta from the nucleus. So on the left, once again going
back to the neutral lithium atom, this electron is in
the second energy level. So it's further away
than this electron. This electron is in the first
energy level, in the 1s2, so this distance here is smaller
than the distance on the left. And so since the
distance is smaller, this electron in
magenta feels more of an attractive force
from the nucleus. Once again, that's
Coulomb's law. And so therefore, there's an
increased attractive force. Therefore, you take more energy
to pull that electron away. So it takes much more energy
to pull the second electron away than the
first, and so that's why we see an increase
in ionization energy. So distance says the fact
that this electron is closer means it takes more
energy to pull it away, and that's another
reason why this number for the second
ionization energy is so much larger than the first. So it takes a heck
of lot more energy to pull away your
second electron. And that explains why we
see lithium forming a plus 1 cation, because it doesn't take
anywhere near as much energy to pull away one electron
as it does to take away two to form a lithium 2 plus. And so this is one way to tell
what kind of an ion will form. Look at the ionization energies,
and when you see a huge jump, that clues you in as to which
ions are easier to form.