Potassium-argon (K-Ar) dating | Cosmology & Astronomy | Khan Academy

We know that an
element is defined by the number of protons it has. For example, potassium. We look at the periodic
table of elements. And I have a snapshot of
it, of not the entire table but part of it here. Potassium has 19 protons. And we could write it like this. And this is a little
bit redundant. We know that if it’s potassium
that atom has 19 protons. And we know if an
atom has 19 protons it is going to be potassium. Now, we also know that not all
of the atoms of a given element have the same
number of neutrons. And when we talk
about a given element, but we have different
numbers of neutrons we call them isotopes
of that element. So for example,
potassium can come in a form that has
exactly 20 neutrons. And we call that potassium-39. And 39, this mass
number, it’s a count of the 19 protons
plus 20 neutrons. And this is actually the most
common isotope of potassium. It accounts for, I’m
just rounding off, 93.3% of the potassium that
you would find on Earth. Now, some of the other
isotopes of potassium. You also have potassium–
and once again writing the K and the 19 are a
little bit redundant– you also have potassium-41. So this would have 22 neutrons. 22 plus 19 is 41. This accounts for about 6.7%
of the potassium on the planet. And then you have a
very scarce isotope of potassium called
potassium-40. Potassium-40 clearly
has 21 neutrons. And it’s very, very,
very, very scarce. It accounts for only 0.0117%
of all the potassium. But this is also the
isotope of potassium that’s interesting to us
from the point of view of dating old, old rock, and
especially old volcanic rock. And as we’ll see, when you
can date old volcanic rock it allows you to date
other types of rock or other types of fossils
that might be sandwiched in between old volcanic rock. And so what’s really interesting
about potassium-40 here is that it has a half-life
of 1.25 billion years. So the good thing about
that, as opposed to something like carbon-14, it can
be used to date really, really, really old things. And every 1.25
billion years– let me write it like this,
that’s its half-life– so 50% of any given
sample will have decayed. And 11% will have
decayed into argon-40. So argon is right over here. It has 18 protons. So when you think about
it decaying into argon-40, what you see is that
it lost a proton, but it has the same mass number. So one of the protons must of
somehow turned into a neutron. And it actually captures
one of the inner electrons, and then it emits
other things, and I won’t go into all the
quantum physics of it, but it turns into argon-40. And 89% turn into calcium-40. And you see calcium on the
periodic table right over here has 20 protons. So this is a situation
where one of the neutrons turns into a proton. This is a situation
where one of the protons turns into a neutron. And what’s really
interesting to us is this part right over here. Because what’s cool about argon,
and we study this a little bit in the chemistry playlist, it is
a noble gas, it is unreactive. And so when it is embedded
in something that’s in a liquid state it’ll
kind of just bubble out. It’s not bonded to
anything, and so it’ll just bubble out and just go
out into the atmosphere. So what’s interesting
about this whole situation is you can imagine what happens
during a volcanic eruption. Let me draw a volcano here. So let’s say that
this is our volcano. And it erupts at some
time in the past. So it erupts, and you have
all of this lava flowing. That lava will contain some
amount of potassium-40. And actually, it’ll
already contain some amount of argon-40. But what’s neat
about argon-40 is that while it’s lava, while it’s
in this liquid state– so let’s imagine this lava
right over here. It’s a bunch of stuff
right over here. I’ll do the potassium-40. And let me do it in a color
that I haven’t used yet. I’ll do the
potassium-40 in magenta. It’ll have some
potassium-40 in it. I’m maybe over doing it. It’s a very scarce isotope. But it’ll have some
potassium-40 in it. And it might already have some
argon-40 in it just like that. But argon-40 is a noble gas. It’s not going to bond anything. And while this lava
is in a liquid state it’s going to be
able to bubble out. It’ll just float to the top. It has no bonds. And it’ll just evaporate. I shouldn’t say evaporate. It’ll just bubble
out essentially, because it’s not
bonded to anything, and it’ll sort of just seep out
while we are in a liquid state. And what’s really
interesting about that is that when you have
these volcanic eruptions, and because this argon-40
is seeping out, by the time this lava has hardened
into volcanic rock– and I’ll do that volcanic
rock in a different color. By the time it has
hardened into volcanic rock all of the argon-40
will be gone. It won’t be there anymore. And so what’s neat is, this
volcanic event, the fact that this rock
has become liquid, it kind of resets the
amount of argon-40 there. So then you’re only going to
be left with potassium-40 here. And that’s why the argon-40
is more interesting, because the calcium-40 won’t
necessarily have seeped out. And there might have already
been calcium-40 here. So it won’t
necessarily seep out. But the argon-40 will seep out. So it kind of resets it. The volcanic event resets
the amount of argon-40. So right when the
event happened, you shouldn’t have any argon-40
right when that lava actually becomes solid. And so if you fast forward
to some future date, and if you look at the sample–
let me copy and paste it. So if you fast forward to
some future date, and you see that there is some
argon-40 there, in that sample, you know this is
a volcanic rock. You know that it was due to
some previous volcanic event. You know that this argon-40 is
from the decayed potassium-40. And you know that it has decayed
since that volcanic event, because if it was there before
it would have seeped out. So the only way that this would
have been able to get trapped is, while it was liquid
it would seep out, but once it’s solid it can
get trapped inside the rock. And so you know the only
way this argon-40 can exist there is by decay
from that potassium-40. So you can look at the ratio. So you know for every
one of these argon-40’s, because only 11% of the decay
products are argon-40’s, for every one of
those you must have on the order of about nine
calcium-40’s that also decayed. And so for every one of these
argon-40’s you know that there must have been 10
original potassium-40’s. And so what you
can do is you can look at the ratio of the
number of potassium-40’s there are today to the number
that there must have been, based on this evidence right
over here, to actually date it. And in the next
video I’ll actually go through the
mathematical calculation to show you that you
can actually date it. And the reason this
is really useful is, you can look
at those ratios. And volcanic eruptions
aren’t happening every day, but if you start looking over
millions and millions of years, on that time scale,
they’re actually happening reasonably frequent. And so let’s dig in the ground. So let’s say this is the
ground right over here. And you dig enough and you
see a volcanic eruption, you see some volcanic
rock right over there, and then you dig even more. There’s another layer of
volcanic rock right over there. So this is another
layer of volcanic rock. So they’re all going to have a
certain amount of potassium-40 in it. This is going to have some
amount of potassium-40 in it. And then let’s say this one
over here has more argon-40. This one has a little bit less. And using the math that we’re
going to do in the next video, let’s say you’re
able to say that this is, using the half-life, and
using the ratio of argon-40 that’s left, or using the
ratio of the potassium-40 left to what you know was there
before, you say that this must have solidified 100
million years ago, 100 million years
before the present. And you know that this layer
right over here solidified. Let’s say, you know it
solidified about 150 million years
before the present. And let’s say you feel pretty
good that this soil hasn’t been dug up and mixed or
anything like that. It looks like it’s been
pretty untouched when you look at these soil
samples right over here. And let’s say you see
some fossils in here. Then, even though carbon-14
dating is kind of useless, really, when you get
beyond 50,000 years, you see these fossils in
between these two periods. It’s a pretty good
indicator, if you can assume that this soil hasn’t
been dug around and mixed, that this fossil is
between 100 million and 150 million years old. This event happened. Then you have these
fossils got deposited. These animals died, or
they lived and they died. And then you had this
other volcanic event. So it allows you, even though
you’re only directly dating the volcanic rock,
it allows you, when you look at the layers,
to relatively date things in between those layer. So it isn’t just about
dating volcanic rock. It allows us to date things
that are very, very, very old and go way further back in time
than just carbon-14 dating.

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