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CATHERINE DRENNAN:
So radioactive decay

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is kind of a classic example
of a first-order process.

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So we are doing one
little tiny section

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of the chapter on
nuclear chemistry,

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and we're doing that all today.

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And so all we're really
covering is problems associated

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with first-order processes.

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So this is just a small
introduction to this idea.

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00:00:49,660 --> 00:00:52,770
So radioactive decay has
a lot of applications.

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00:00:52,770 --> 00:00:56,910
There are medical applications,
including imaging organs

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and bones, including the heart.

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And so there is a compound
that you already saw

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called Cardiolite.

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And so we talked about
this in transition metals

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because you have a
transition metal.

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And what is the geometry
of this compound?

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Octahedral, and we have
cyanide ligands, which

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what kind of field strength?

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Strong.

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Yeah.

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So this compound
was designed in part

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by an MIT professor,
Alan Davison.

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You could go talk to him about
this incredible discovery

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and invention.

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It's used about seven
million times a year

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or to image various organs and
has been for a very long time.

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00:01:39,160 --> 00:01:41,500
It's off patent now.

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00:01:41,500 --> 00:01:45,970
But this patent made Allen
Davison, MIT, and MIT Chemistry

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00:01:45,970 --> 00:01:48,020
Department an enormous
amount of money.

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00:01:48,020 --> 00:01:49,740
And so you could go
talk to him about it,

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except he's happily retired
living in one of his homes.

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[LAUGHTER]

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00:01:54,520 --> 00:01:56,520
So you can't really do that.

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00:01:56,520 --> 00:02:00,360
But anyway, so this uses
an isotope of technetium,

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which is metastable isotope.

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And so it's 99.

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00:02:04,280 --> 00:02:11,160
It's an isotope of the
normal 98 atomic mass.

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00:02:11,160 --> 00:02:12,670
And so the next
challenge, you're

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always looking for
the next great thing,

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00:02:15,220 --> 00:02:16,760
the next great imaging agent.

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00:02:16,760 --> 00:02:20,260
So this is still a very
active area of research,

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and there's actually a talk just
this week on campus about work

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00:02:23,730 --> 00:02:24,760
in this area.

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00:02:24,760 --> 00:02:28,190
So this is transition metals
combined with radioactivity.

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00:02:28,190 --> 00:02:32,130
So it's two topics
here in the class.

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00:02:32,130 --> 00:02:34,310
So another, of
course, important use

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is the potential
of nuclear energy

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and the current use
of nuclear energy.

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This has many
challenges, and I don't

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want to go on record of what
I think about nuclear energy.

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00:02:43,330 --> 00:02:45,530
I think it's a
complicated problem.

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There are a lot of challenges.

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But one I'd like to
bring up, because I think

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it's particularly
interesting to me,

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is what to do with the waste.

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And so one story that I
heard about actually there

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was a documentary
made about this.

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Finland had this idea to create
this three-mile long tunnel,

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and they wanted to store 12,000
metric tons of nuclear waste.

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And they wanted the containers
to store it for 100,000 years.

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And this documentary asked
a number of questions

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about this idea, such as, what
kind of container do you use,

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and how do you know the material
you design your container is

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going to last 100,000 years?

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As experimental
scientists, we like

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to test how long things last.

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But you can't really
do this experiment.

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Also, it kind of
brought up the idea,

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do you guard this facility
for 100,000 years?

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Because you can make bombs out
of a lot of this radioactive

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waste.

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So you kind of
need to protect it.

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But maybe you
should just bury it

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and then no one knows
it's there so you

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don't have to guard it so
they can't find it and use it.

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But then what if
someone stumbles upon it

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and releases all of
this radioactivity?

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So that would be bad.

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So do you put warning
signs for people

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who will be around 100,000 years
from now, saying, hey, don't

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go in here.

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00:04:07,780 --> 00:04:09,150
It looks like a pretty tunnel.

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00:04:09,150 --> 00:04:13,470
But, hey, the half-life
of the thing stored here

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are 100,000 years.

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So this is pretty
radioactive still.

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00:04:16,630 --> 00:04:17,740
Don't go inside.

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00:04:17,740 --> 00:04:20,959
And if you write this sign,
what language do you put it in?

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So the documentary pointed
out that Neanderthals

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00:04:25,630 --> 00:04:28,500
existed like 40,000 years ago.

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00:04:28,500 --> 00:04:32,790
So 100,000 years from now,
what's going to be going on?

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00:04:32,790 --> 00:04:36,070
How do you write a sign to
people that long in the future?

99
00:04:36,070 --> 00:04:39,130
Anyway, I just think that these
are sort of interesting ideas

100
00:04:39,130 --> 00:04:42,740
and brings up the point that
as scientists and engineers,

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00:04:42,740 --> 00:04:44,720
we need to think not
only about the science

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00:04:44,720 --> 00:04:46,250
and engineering of
what we're doing,

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but the ramifications to
society and the sociology

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00:04:51,660 --> 00:04:54,990
as well as politics involved
in some of this science.

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So this is an interesting
area for that intersection

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00:04:57,970 --> 00:05:00,950
of the social sciences
and the natural sciences

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00:05:00,950 --> 00:05:02,980
and engineering.

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00:05:02,980 --> 00:05:06,690
So radioactive
decay-- definitely

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00:05:06,690 --> 00:05:11,140
a useful thing, dangerous and
useful all at the same time.

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00:05:11,140 --> 00:05:11,935
Oh, look at that.

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00:05:11,935 --> 00:05:13,725
You know the clicker
question's coming up

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00:05:13,725 --> 00:05:15,330
at the bottom of the page.

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00:05:15,330 --> 00:05:16,171
We're not there yet.

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00:05:16,171 --> 00:05:16,670
It's OK.

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00:05:16,670 --> 00:05:19,179
We're not there yet.

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00:05:19,179 --> 00:05:20,970
I just added that at
the end and apparently

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00:05:20,970 --> 00:05:23,130
didn't animate it well.

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So the decay of a nucleus is
independent of how many nuclei

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are around it.

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00:05:28,450 --> 00:05:30,940
That's what makes it
a first-order process.

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00:05:30,940 --> 00:05:32,990
So because it's a
first-order process,

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00:05:32,990 --> 00:05:36,740
we can apply those first-order
integrated rate laws

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00:05:36,740 --> 00:05:38,550
that we just derived.

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00:05:38,550 --> 00:05:41,950
So we had our rate log of the
concentration of something

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00:05:41,950 --> 00:05:45,170
A equals its original
concentration

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00:05:45,170 --> 00:05:49,370
to the e to minus k, which is
our rate constant times time

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00:05:49,370 --> 00:05:53,240
and also our half-life
equation that we just used.

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So instead of
concentration of A,

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00:05:55,945 --> 00:05:58,430
though, we're going to
have a different thing

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00:05:58,430 --> 00:06:02,050
to express what we're
interested in here, which

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00:06:02,050 --> 00:06:05,020
is N, the number of nuclei.

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00:06:05,020 --> 00:06:08,990
So we can just write that
same expression down.

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00:06:08,990 --> 00:06:10,640
But instead of
concentration of A,

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00:06:10,640 --> 00:06:12,750
we're just going to
use capital N. So

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00:06:12,750 --> 00:06:15,570
N, the number of nuclei
at some particular time,

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00:06:15,570 --> 00:06:19,680
equals how many nuclei were
present originally times e

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00:06:19,680 --> 00:06:21,010
to the minus k.

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00:06:21,010 --> 00:06:23,080
And here it is a
rate constant still,

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00:06:23,080 --> 00:06:26,480
but it's a decay constant in
that the rate you're measuring

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00:06:26,480 --> 00:06:28,290
is radioactive decay.

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00:06:28,290 --> 00:06:29,760
So it kind of has
a special name.

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00:06:29,760 --> 00:06:31,593
Although, if you use
rate constant for that,

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that is what it
is, so that's OK.

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00:06:34,480 --> 00:06:35,820
t is still time.

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00:06:35,820 --> 00:06:40,870
And yes, N to the o is the
original number of nuclei.

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00:06:40,870 --> 00:06:43,240
So we're just going to
do a clicker question

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00:06:43,240 --> 00:06:45,530
about how one goes
about calculating

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00:06:45,530 --> 00:06:46,940
the number of nuclei.

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00:06:58,670 --> 00:06:59,363
10 more seconds.

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00:07:16,080 --> 00:07:21,790
So someone want to tell me
for one of the Green Lantern

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00:07:21,790 --> 00:07:29,450
T-shirts, what is wrong
with the other answers?

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I think I saw your
hand up first.

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Sorry, folks.

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AUDIENCE: Let's see.

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So answers one
and two, they have

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the wrong-- what was it--
the molar mass of technetium.

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Is that technetium?

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Yeah And answer four does not
multiply by Avogadro's number.

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00:07:50,352 --> 00:07:52,310
So that's going to give
you the number of moles

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of the particle.

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CATHERINE DRENNAN: Right.

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Great job.

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It's Thanksgiving.

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I thought we needed
a good prize today.

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So right.

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00:08:02,060 --> 00:08:05,110
So one thing you
also want to remember

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00:08:05,110 --> 00:08:07,740
make sure that your
units are good.

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00:08:07,740 --> 00:08:09,770
And it's really
important in doing

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00:08:09,770 --> 00:08:12,890
this-- you can take
this back-- to remember

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00:08:12,890 --> 00:08:18,990
to use the number that is here,
this atomic mass number, not

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00:08:18,990 --> 00:08:23,786
the one from the periodic table
in calculating the problem.

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00:08:23,786 --> 00:08:25,910
Actually, the periodic
table disappeared from that.

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Oh, well.

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00:08:26,910 --> 00:08:30,940
So if you use the periodic
table, it's a close answer

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00:08:30,940 --> 00:08:32,340
but sometimes.

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00:08:32,340 --> 00:08:34,080
Sometimes it won't be so close.

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But remember, when it tells
you about the isotope,

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00:08:37,590 --> 00:08:40,880
it always has the
atomic mass that you

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00:08:40,880 --> 00:08:43,780
should be using in the problem
as part of the questions.

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00:08:43,780 --> 00:08:45,610
So keep that in mind.

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00:08:45,610 --> 00:08:48,370
And yeah, you definitely want
to remember Avogadro's number.

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00:08:48,370 --> 00:08:49,930
And the answers
are such that it's

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00:08:49,930 --> 00:08:51,679
hard to tell that you messed up.

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00:08:51,679 --> 00:08:53,220
With the wavelength,
it's really easy

185
00:08:53,220 --> 00:08:55,410
to tell you messed up if you
didn't use Avogadro's number

186
00:08:55,410 --> 00:08:56,826
because it doesn't
make any sense.

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00:08:56,826 --> 00:08:58,920
With these, it's
a little harder.

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00:08:58,920 --> 00:09:02,180
So remember to use the
isotope's atomic mass

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00:09:02,180 --> 00:09:04,180
and also remember to
use Avogadro's number

190
00:09:04,180 --> 00:09:05,190
when doing this.

191
00:09:05,190 --> 00:09:08,610
And then you should be fine.

192
00:09:08,610 --> 00:09:10,140
So this is really similar.

193
00:09:10,140 --> 00:09:12,140
It's really similar,
depending on whether you're

194
00:09:12,140 --> 00:09:16,160
talking about chemical
kinetics or nuclear kinetics

195
00:09:16,160 --> 00:09:20,020
in doing these problems
in terms of the equations.

196
00:09:20,020 --> 00:09:25,650
But in chemical kinetics, you're
measuring the concentration.

197
00:09:25,650 --> 00:09:30,080
Whereas with nuclear kinetics,
you're measuring decay events.

198
00:09:30,080 --> 00:09:33,080
And so usually how do
you measure decay events?

199
00:09:33,080 --> 00:09:38,020
And the most common way is
here, our Geiger counter.

200
00:09:38,020 --> 00:09:40,530
So I just want to-- it's
always important every once

201
00:09:40,530 --> 00:09:42,410
in a while at MIT
to double check

202
00:09:42,410 --> 00:09:45,030
that the rooms that
you're teaching in

203
00:09:45,030 --> 00:09:48,440
have not been contaminated by
some wonderful experiments.

204
00:09:48,440 --> 00:09:49,810
So, so far, we're good.

205
00:09:49,810 --> 00:09:52,220
So here, this is working.

206
00:09:52,220 --> 00:09:54,000
You can hear the chips, I think.

207
00:09:54,000 --> 00:09:55,211
This is pretty good.

208
00:09:55,211 --> 00:09:56,960
You don't have to be
concerned about this.

209
00:09:56,960 --> 00:09:58,501
There's always some
background level.

210
00:09:58,501 --> 00:09:59,240
It's fine.

211
00:09:59,240 --> 00:10:05,240
So there are gases in
here that will get ionized

212
00:10:05,240 --> 00:10:06,920
by radiation, which gives off.

213
00:10:06,920 --> 00:10:09,120
Then that's translated
into that clicking noise.

214
00:10:09,120 --> 00:10:10,450
So that's what is happening.

215
00:10:10,450 --> 00:10:13,090
So it's measuring,
with our thing,

216
00:10:13,090 --> 00:10:16,890
whether there are any
radioactive events going on.

217
00:10:16,890 --> 00:10:18,800
And this is called
a Geiger counter.

218
00:10:18,800 --> 00:10:21,040
And we use X-rays in my lab.

219
00:10:21,040 --> 00:10:24,850
So I went and stole this
from our X-ray facility

220
00:10:24,850 --> 00:10:25,730
before I came here.

221
00:10:25,730 --> 00:10:27,146
Luckily, it's
almost Thanksgiving,

222
00:10:27,146 --> 00:10:29,040
so no one was
collecting any data.

223
00:10:29,040 --> 00:10:32,850
So no one will get in trouble
for taking this right now.

224
00:10:32,850 --> 00:10:35,720
And Hans Geiger is
the person who came up

225
00:10:35,720 --> 00:10:37,940
with this idea and this device.

226
00:10:37,940 --> 00:10:40,480
Does anyone remember where
we heard that name before?

227
00:10:40,480 --> 00:10:44,000
Think back class two.

228
00:10:44,000 --> 00:10:48,600
So he did that amazing
gold foil experiment.

229
00:10:48,600 --> 00:10:51,810
And so our ping pong balls
that we were throwing

230
00:10:51,810 --> 00:10:53,740
were duplicating the
experiment that he

231
00:10:53,740 --> 00:10:55,310
did as a graduate student.

232
00:10:55,310 --> 00:10:57,160
And luckily, I think
he was smart enough

233
00:10:57,160 --> 00:10:59,430
to realize that when you're
working with things--

234
00:10:59,430 --> 00:11:02,110
he was working with a lot of
radioactivity at that point--

235
00:11:02,110 --> 00:11:04,570
that once you know exactly
how much radioactivity you're

236
00:11:04,570 --> 00:11:08,710
working with-- and so these
were very early day experiments.

237
00:11:08,710 --> 00:11:11,550
And he came up with
this device that helped

238
00:11:11,550 --> 00:11:12,850
him know how safe he was.

239
00:11:12,850 --> 00:11:16,490
And this is still sort
of the standard thing

240
00:11:16,490 --> 00:11:20,030
to have these around and
double check that there

241
00:11:20,030 --> 00:11:22,530
is no radiation leaks
in places like that.

242
00:11:22,530 --> 00:11:25,140
So the Geiger
counter-- all right.

243
00:11:25,140 --> 00:11:30,160
So also a couple of
more terminology things.

244
00:11:30,160 --> 00:11:33,970
Decay rate is also called
activity or specific activity.

245
00:11:33,970 --> 00:11:37,600
So you're talking about how
active your substance is.

246
00:11:37,600 --> 00:11:41,470
That's really how
radioactive is it.

247
00:11:41,470 --> 00:11:44,370
And activity also
has the letter A.

248
00:11:44,370 --> 00:11:46,480
So we were talking about
the concentration of A.

249
00:11:46,480 --> 00:11:47,480
Now we have A again.

250
00:11:47,480 --> 00:11:49,550
There's a lot of
A's in this unit.

251
00:11:49,550 --> 00:11:54,810
So that's the change now in
the number of nuclei over time-

252
00:11:54,810 --> 00:11:58,310
that's the rate expression,
or the rate law-- k,

253
00:11:58,310 --> 00:12:01,490
the decay constant, times
the number of nuclei.

254
00:12:01,490 --> 00:12:04,900
And because activity is
proportional to the number

255
00:12:04,900 --> 00:12:08,230
of nuclei, we can also
take this expression

256
00:12:08,230 --> 00:12:11,600
that we had before
that had the N's in it

257
00:12:11,600 --> 00:12:12,740
and rewrite it with A.

258
00:12:12,740 --> 00:12:15,990
So now it's really just like
that first-order expression

259
00:12:15,990 --> 00:12:19,210
we had but without the
concentration term.

260
00:12:19,210 --> 00:12:22,830
So we have the activity
at some time equals

261
00:12:22,830 --> 00:12:26,180
the original activity
of the material times

262
00:12:26,180 --> 00:12:27,930
e to the minus kt.

263
00:12:27,930 --> 00:12:29,880
And all of these
equations are going

264
00:12:29,880 --> 00:12:32,400
to be on your equation sheet.

265
00:12:32,400 --> 00:12:35,080
But if you mess up and use
the wrong equation for this,

266
00:12:35,080 --> 00:12:36,580
it doesn't matter,
as long as you're

267
00:12:36,580 --> 00:12:39,010
using the first-order equation.

268
00:12:39,010 --> 00:12:41,680
Whether it's
concentration or activity,

269
00:12:41,680 --> 00:12:44,820
it's the same idea
that you can determine,

270
00:12:44,820 --> 00:12:47,710
if you know the rate constant
or the decay constant,

271
00:12:47,710 --> 00:12:51,210
how much material is left,
how much activity is left,

272
00:12:51,210 --> 00:12:56,320
how many nuclei are left
after a given amount of time.

273
00:12:56,320 --> 00:12:58,000
So I know what you're
all thinking now.

274
00:12:58,000 --> 00:13:00,000
You're thinking,
this is fantastic,

275
00:13:00,000 --> 00:13:02,540
but what about the units?

276
00:13:02,540 --> 00:13:05,370
We musts here about the units.

277
00:13:05,370 --> 00:13:11,890
So the SI units for activity
are the becquerel, BQ.

278
00:13:11,890 --> 00:13:16,230
And one becquerel is one
radioactive disintegration

279
00:13:16,230 --> 00:13:18,140
per second.

280
00:13:18,140 --> 00:13:20,560
And this is the newer unit.

281
00:13:20,560 --> 00:13:23,480
The older unit was
called a curie,

282
00:13:23,480 --> 00:13:26,930
and sometimes you will still
see this in the literature.

283
00:13:26,930 --> 00:13:31,120
And a curie, one
curie, was 3.7 times 10

284
00:13:31,120 --> 00:13:34,110
to the 10th
disintegrations per second.

285
00:13:34,110 --> 00:13:39,020
So it was a much larger number
than the current SI unit.

286
00:13:39,020 --> 00:13:44,100
So this was what one gram of a
radium specific activity was.

287
00:13:44,100 --> 00:13:45,760
So they used this big number.

288
00:13:45,760 --> 00:13:48,230
But it was not really
practical because you

289
00:13:48,230 --> 00:13:51,030
want to tell people like how
much radiation would be safe

290
00:13:51,030 --> 00:13:53,350
for them to have in a year
or something like that.

291
00:13:53,350 --> 00:13:56,900
And you didn't want to use
this giant number for that.

292
00:13:56,900 --> 00:13:58,830
So we've moved to here.

293
00:13:58,830 --> 00:14:04,920
So does anyone know or want to
guess who the older unit was

294
00:14:04,920 --> 00:14:08,950
named for of radioactivity?

295
00:14:08,950 --> 00:14:11,000
One might think Marie Curie.

296
00:14:11,000 --> 00:14:13,160
But a lot of the
evidence suggests

297
00:14:13,160 --> 00:14:16,720
it was actually her
husband, Pierre Curie,

298
00:14:16,720 --> 00:14:17,820
who it was named after.

299
00:14:17,820 --> 00:14:19,800
It's a bit controversial.

300
00:14:19,800 --> 00:14:21,600
But they both worked
together, and they

301
00:14:21,600 --> 00:14:24,250
worked with Henri Becquerel.

302
00:14:24,250 --> 00:14:26,850
And they all won
the 1983 Nobel Prize

303
00:14:26,850 --> 00:14:28,970
for discovering radioactivity.

304
00:14:28,970 --> 00:14:34,390
Three years later, Pierre Curie
was killed crossing the street.

305
00:14:34,390 --> 00:14:39,100
He slipped when it was raining,
and a horse and wagon, I guess,

306
00:14:39,100 --> 00:14:41,650
ran over him and killed him.

307
00:14:41,650 --> 00:14:46,400
So this is, I think, an example
of someone who's so brilliant,

308
00:14:46,400 --> 00:14:47,970
but you say, they're
so brilliant,

309
00:14:47,970 --> 00:14:50,810
but do they look both ways
before they cross the street?

310
00:14:50,810 --> 00:14:52,430
So you are all very brilliant.

311
00:14:52,430 --> 00:14:54,600
And I encourage
you look both ways

312
00:14:54,600 --> 00:14:56,410
before you cross the street.

313
00:14:56,410 --> 00:14:58,610
Anyway, so he died.

314
00:14:58,610 --> 00:15:02,290
And some of the stories are that
they named the unit after him

315
00:15:02,290 --> 00:15:03,480
as a tribute.

316
00:15:03,480 --> 00:15:05,780
Others say, well, it's
really for both of them.

317
00:15:05,780 --> 00:15:08,545
But in any case, now it's
named after the third person,

318
00:15:08,545 --> 00:15:09,341
Henri Becquerel.

319
00:15:13,620 --> 00:15:16,810
So radioactivity,
I'm going to tell you

320
00:15:16,810 --> 00:15:19,350
a little bit about
radioactivity.

321
00:15:19,350 --> 00:15:21,170
This chart is not
in your handout

322
00:15:21,170 --> 00:15:23,280
because you're not
responsible for knowing

323
00:15:23,280 --> 00:15:27,500
all this information, so I
just didn't put it in there.

324
00:15:27,500 --> 00:15:29,299
But you can look this up.

325
00:15:29,299 --> 00:15:30,840
There's a couple of
points I did make

326
00:15:30,840 --> 00:15:33,160
in your handout,
which is there are

327
00:15:33,160 --> 00:15:39,330
different types of
nuclear radiation.

328
00:15:39,330 --> 00:15:43,650
We have alpha particles, alpha
decay, beta decay, gamma decay.

329
00:15:43,650 --> 00:15:45,940
Some of those involve
a mass change.

330
00:15:45,940 --> 00:15:49,850
So like an alpha particle is
the same as a helium-4 nucleus--

331
00:15:49,850 --> 00:15:52,880
two protons, two neutrons.

332
00:15:52,880 --> 00:15:55,580
Beta decay involves an electron.

333
00:15:55,580 --> 00:15:58,220
Gamma is a photon.

334
00:15:58,220 --> 00:16:00,180
So there are definitely
different types.

335
00:16:00,180 --> 00:16:03,310
Some mass change, some not.

336
00:16:03,310 --> 00:16:07,900
There are also really dramatic
differences in half-life.

337
00:16:07,900 --> 00:16:10,500
So again, half-life depends
on the material in question.

338
00:16:10,500 --> 00:16:14,020
It depends on that decay
constant, that rate constant.

339
00:16:14,020 --> 00:16:16,500
And if we look at this
table, we can see things

340
00:16:16,500 --> 00:16:18,490
from milli seconds.

341
00:16:18,490 --> 00:16:22,395
And if we look at some
of these, d is for a day.

342
00:16:22,395 --> 00:16:24,190
a is for year.

343
00:16:24,190 --> 00:16:25,570
y is also for year.

344
00:16:25,570 --> 00:16:27,710
So sometimes you'll
see y for year.

345
00:16:27,710 --> 00:16:29,025
Sometimes you'll see a.

346
00:16:29,025 --> 00:16:32,280
I think most people guess
that y is for a year.

347
00:16:32,280 --> 00:16:34,680
That a is for year,
I don't really know.

348
00:16:34,680 --> 00:16:36,720
But anyway, in
this table it's a.

349
00:16:36,720 --> 00:16:38,840
So if you see that,
don't be confused.

350
00:16:38,840 --> 00:16:44,860
And Ga, that's giga
years, so 10 to the ninth.

351
00:16:44,860 --> 00:16:48,740
That's where the
Finland 100,000 years

352
00:16:48,740 --> 00:16:52,940
comes from, that we need to
keep the stuff safe for a very,

353
00:16:52,940 --> 00:16:56,650
very, very, very, very,
very long amount of time

354
00:16:56,650 --> 00:16:59,640
for giga years.

355
00:16:59,640 --> 00:17:05,569
So in some decay processes,
such as uranium-238,

356
00:17:05,569 --> 00:17:10,770
you have more than one type
of nuclear radiation going on.

357
00:17:10,770 --> 00:17:15,510
And it can involve a very
long and complicated series

358
00:17:15,510 --> 00:17:17,569
of different events.

359
00:17:17,569 --> 00:17:20,819
So here at MIT, we spend
most of our time talking

360
00:17:20,819 --> 00:17:22,540
about science and engineering.

361
00:17:22,540 --> 00:17:24,099
But I feel like
every once in a while

362
00:17:24,099 --> 00:17:28,540
we should throw in some poetry
into our science classes.

363
00:17:28,540 --> 00:17:33,570
So once a year I like
to read a chemistry poem

364
00:17:33,570 --> 00:17:35,590
to enrich our lives.

365
00:17:35,590 --> 00:17:40,549
And today is that day in 2014.

366
00:17:40,549 --> 00:17:42,090
And the poem I'm
going to read to you

367
00:17:42,090 --> 00:17:46,330
is called "The Days
of Our Half-Lives,"

368
00:17:46,330 --> 00:17:49,870
and it is by Professor
Mala Radhakrishnan.

369
00:17:49,870 --> 00:17:54,430
She got her PhD here at MIT
in the Chemistry department.

370
00:17:54,430 --> 00:17:57,950
And she wrote this book, which
she wanted me to point out

371
00:17:57,950 --> 00:18:01,260
is available on Amazon if you're
looking for a Christmas present

372
00:18:01,260 --> 00:18:05,250
for a very, very
geeky friend of yours.

373
00:18:05,250 --> 00:18:08,230
And it's illustrated by
another MIT chemistry

374
00:18:08,230 --> 00:18:11,560
PhD, Mary O'Reilly, who
actually did the illustrations

375
00:18:11,560 --> 00:18:13,870
for the videos that I've
been showing you in class.

376
00:18:13,870 --> 00:18:19,760
So MIT chemists, just really
multi-talented individuals.

377
00:18:19,760 --> 00:18:22,520
So I will read
you this poem now.

378
00:18:22,520 --> 00:18:26,240
And as I read it to
you, I will point out

379
00:18:26,240 --> 00:18:29,730
what is happening in
this decay process

380
00:18:29,730 --> 00:18:35,200
because all of Mala's poetry
is scientifically correct.

381
00:18:39,620 --> 00:18:44,480
So "Days of Our Half-lives."

382
00:18:44,480 --> 00:18:47,510
"My dearest love, I am
writing you to tell you

383
00:18:47,510 --> 00:18:49,470
all that I've been through.

384
00:18:49,470 --> 00:18:52,370
I've changed my whole identity.

385
00:18:52,370 --> 00:18:55,690
But loved, I can't
pretend to be.

386
00:18:55,690 --> 00:19:00,620
When I was uranium-238,
you were on my case

387
00:19:00,620 --> 00:19:03,020
to start losing weight.

388
00:19:03,020 --> 00:19:06,340
For 5 billion years I'd
hoped and I'd prayed,

389
00:19:06,340 --> 00:19:10,620
and finally I had
an alpha decay.

390
00:19:10,620 --> 00:19:15,380
Two protons and two neutrons
went right out the door.

391
00:19:15,380 --> 00:19:19,250
And now I was thorium-234.

392
00:19:19,250 --> 00:19:22,580
But my nucleus was still
unfit for your eyes,

393
00:19:22,580 --> 00:19:26,210
not positive enough
for its large size.

394
00:19:26,210 --> 00:19:29,240
But this time my half-life
was not very long,

395
00:19:29,240 --> 00:19:32,330
because my will to change
was really quite strong.

396
00:19:32,330 --> 00:19:36,790
It took just a month, not even
a millennium, to beta decay

397
00:19:36,790 --> 00:19:39,540
into protactinium.

398
00:19:39,540 --> 00:19:44,310
But still, rejected me right off
the bat-- protactinium, who's

399
00:19:44,310 --> 00:19:45,790
heard of that?

400
00:19:45,790 --> 00:19:53,270
So beta decay I did once
more to become uranium-234.

401
00:19:53,270 --> 00:19:57,480
Myself again but a new isotope,
you still weren't satisfied.

402
00:19:57,480 --> 00:19:59,480
But I still had hope.

403
00:19:59,480 --> 00:20:02,340
Three alpha decays
'twas hard, but I

404
00:20:02,340 --> 00:20:11,020
stayed on through thorium
then radium and then radon.

405
00:20:11,020 --> 00:20:14,060
I thought that I would
finally please you.

406
00:20:14,060 --> 00:20:17,840
My mass was a healthy 222.

407
00:20:17,840 --> 00:20:22,580
But you said, although
I like your mass,

408
00:20:22,580 --> 00:20:25,223
I don't want to be
with a noble gas.

409
00:20:28,990 --> 00:20:30,016
They dress so well.

410
00:20:33,120 --> 00:20:35,150
You had a point though.

411
00:20:35,150 --> 00:20:37,100
I wasn't reactive.

412
00:20:37,100 --> 00:20:40,420
So in order to please
you, I stayed proactive.

413
00:20:40,420 --> 00:20:43,900
A few days later, I found
you and said, two more alpha

414
00:20:43,900 --> 00:20:47,470
decays, and now I am lead.

415
00:20:49,980 --> 00:20:52,260
But you shook your head.

416
00:20:52,260 --> 00:20:56,850
You were not too keen on
my mass number of 214.

417
00:20:56,850 --> 00:20:59,910
I had a bad experience
with that mass before,

418
00:20:59,910 --> 00:21:04,388
and an unstable astatine
walked right out the door.

419
00:21:04,388 --> 00:21:06,840
So in order to
change, I went away.

420
00:21:06,840 --> 00:21:09,730
But all I could do
was just beta decay.

421
00:21:09,730 --> 00:21:12,250
My hopes and my dreams
started to go under,

422
00:21:12,250 --> 00:21:16,870
because beta decay does
not change a mass number.

423
00:21:16,870 --> 00:21:22,850
To bismuth and polonium,
I hoped and I beckoned.

424
00:21:22,850 --> 00:21:26,520
My half-life was 1
6 4 microseconds.

425
00:21:26,520 --> 00:21:28,600
And then finally,
I alpha decayed.

426
00:21:28,600 --> 00:21:36,100
And then I was lead with a
prize worthy mass of 210.

427
00:21:36,100 --> 00:21:39,120
Got to admit, I was
getting quite tired,

428
00:21:39,120 --> 00:21:42,940
and my patience with
you had nearly expired.

429
00:21:42,940 --> 00:21:45,610
You were more demanding
than any I'd dated.

430
00:21:45,610 --> 00:21:49,790
And much of my energy
had been liberated.

431
00:21:49,790 --> 00:21:52,700
But you still weren't
happy, but you had a fix.

432
00:21:52,700 --> 00:21:56,020
I really like the number 206.

433
00:21:56,020 --> 00:21:57,960
So I waited for
years until the day

434
00:21:57,960 --> 00:22:03,800
which began with another
beta decay and then one more.

435
00:22:03,800 --> 00:22:06,950
And finally, in
the end, I alpha-ed

436
00:22:06,950 --> 00:22:09,970
to lead 206, my friend.

437
00:22:09,970 --> 00:22:11,200
To change any further.

438
00:22:11,200 --> 00:22:15,750
I wouldn't be able-- not longer
active, but happily stable.

439
00:22:15,750 --> 00:22:17,380
It took me a
million years to do,

440
00:22:17,380 --> 00:22:21,360
but look how I've changed,
and all just for you.

441
00:22:21,360 --> 00:22:23,240
Wait, what did you say?

442
00:22:23,240 --> 00:22:26,120
I've gotten so old
that you'd rather

443
00:22:26,120 --> 00:22:29,400
be with a young lass of gold?

444
00:22:29,400 --> 00:22:30,430
Well, I give up.

445
00:22:30,430 --> 00:22:32,020
We're through, my pumpkin.

446
00:22:32,020 --> 00:22:35,380
Shouldn't all my effort
be counting for something?

447
00:22:35,380 --> 00:22:38,310
Well, you won't be able
to rule me anymore,

448
00:22:38,310 --> 00:22:44,840
because I'm leaving you
not for one atom, but four.

449
00:22:44,840 --> 00:22:47,070
That's right.

450
00:22:47,070 --> 00:22:51,380
While you were away
diffusing, I found

451
00:22:51,380 --> 00:22:54,625
some chlorines that I
found quite amusing.

452
00:22:57,170 --> 00:23:02,070
And we're going
to form lead, Cl4,

453
00:23:02,070 --> 00:23:04,800
and you won't be
hearing from me anymore.

454
00:23:04,800 --> 00:23:06,800
See, over the years,
I've grown quite wise.

455
00:23:06,800 --> 00:23:09,430
I've learned that
love's about compromise.

456
00:23:09,430 --> 00:23:11,450
You still have half
of your half-lives

457
00:23:11,450 --> 00:23:13,880
to live, so go out there.

458
00:23:13,880 --> 00:23:18,050
It's your turn to give."

459
00:23:18,050 --> 00:23:19,810
Thank you.

460
00:23:19,810 --> 00:23:23,680
[APPLAUSE]

461
00:23:25,690 --> 00:23:27,941
There's a whole book
of them on Amazon.

462
00:23:32,050 --> 00:23:35,920
So that is first order.

463
00:23:35,920 --> 00:23:38,600
First order is pretty exciting
because it has nuclear decay.

464
00:23:38,600 --> 00:23:40,540
Second order-- not
quite as exciting.

465
00:23:40,540 --> 00:23:43,750
But we should talk
about it anyway.

466
00:23:43,750 --> 00:23:47,399
So second order
integrated rate loss--

467
00:23:47,399 --> 00:23:49,190
we're not going to go
through a derivation.

468
00:23:49,190 --> 00:23:50,850
It's in your book.

469
00:23:50,850 --> 00:23:54,380
But here is the equation,
if you do the derivation.

470
00:23:54,380 --> 00:23:59,060
So now we have 1 over the
concentration of A at time t

471
00:23:59,060 --> 00:24:03,210
equals rate constant
k times t plus 1

472
00:24:03,210 --> 00:24:09,610
over the original
concentration of A.

473
00:24:09,610 --> 00:24:14,590
And we could plot this one over
concentration of t versus time.

474
00:24:14,590 --> 00:24:17,242
And if we did that, you
would have the opportunity

475
00:24:17,242 --> 00:24:18,450
for another clicker question.

476
00:24:30,260 --> 00:24:31,071
10 more seconds.

477
00:24:44,470 --> 00:24:46,570
90s, yeah-- it's kind
of hard to come up

478
00:24:46,570 --> 00:24:48,870
with clicker questions
in this unit, so.

479
00:24:48,870 --> 00:24:53,460
But it's fun, for Thanksgiving,
we'll have lots of 90s.

480
00:24:53,460 --> 00:24:56,730
So we can just look, and this
is actually an expression

481
00:24:56,730 --> 00:24:58,360
for a straight line again.

482
00:24:58,360 --> 00:25:03,310
So we're plotting on the y-axis
one over a concentration of A

483
00:25:03,310 --> 00:25:07,500
at all the various different
times versus time over here.

484
00:25:07,500 --> 00:25:09,540
And so our intercept
is going to be

485
00:25:09,540 --> 00:25:12,120
1 over the initial
concentration of A.

486
00:25:12,120 --> 00:25:15,670
And our slope is
going to be what?

487
00:25:15,670 --> 00:25:17,600
k, right.

488
00:25:17,600 --> 00:25:21,120
So again, you can measure
your concentration

489
00:25:21,120 --> 00:25:24,710
as it changes with time, how
the concentration changes,

490
00:25:24,710 --> 00:25:28,070
plot it, and just determine
your rate constant

491
00:25:28,070 --> 00:25:31,710
for that particular material.

492
00:25:31,710 --> 00:25:37,850
So second order half-life--
we can do another derivation.

493
00:25:37,850 --> 00:25:42,160
But in this case, I will
just give you the equation.

494
00:25:42,160 --> 00:25:46,440
So half-life equals
1 over k times

495
00:25:46,440 --> 00:25:49,370
your original
concentration of A.

496
00:25:49,370 --> 00:25:52,720
And so this is different
from first order.

497
00:25:52,720 --> 00:25:56,050
There is a concentration
term in the equation.

498
00:25:56,050 --> 00:25:58,780
So for second
order half-life, it

499
00:25:58,780 --> 00:26:01,440
does depend on the
starting concentration.

500
00:26:01,440 --> 00:26:02,940
So that's really
the big difference.

501
00:26:02,940 --> 00:26:04,536
In first order,
it doesn't depend

502
00:26:04,536 --> 00:26:05,785
on the starting concentration.

503
00:26:05,785 --> 00:26:08,510
It just depends on the rate
constant or the decay constant,

504
00:26:08,510 --> 00:26:10,430
which depends on the
material in question.

505
00:26:10,430 --> 00:26:12,440
With second order,
you do need to know

506
00:26:12,440 --> 00:26:14,890
how much you had originally.

507
00:26:14,890 --> 00:26:17,430
So again, how do you know if
it's a first or a second order

508
00:26:17,430 --> 00:26:18,760
process?

509
00:26:18,760 --> 00:26:22,630
And here, you really have to
determine it experimentally.

510
00:26:22,630 --> 00:26:24,530
So one thing you
could do is measure

511
00:26:24,530 --> 00:26:28,550
how A changes over time and
then plot your data using

512
00:26:28,550 --> 00:26:30,530
the equation for first order.

513
00:26:30,530 --> 00:26:33,680
And you may see that,
yeah, that does not

514
00:26:33,680 --> 00:26:35,990
form a straight line
when you're plotting

515
00:26:35,990 --> 00:26:38,210
with natural log of
a concentration of A.

516
00:26:38,210 --> 00:26:42,100
But then if you try plotting it
1 over the concentration of A,

517
00:26:42,100 --> 00:26:44,760
you get a beautiful straight
line with your data.

518
00:26:44,760 --> 00:26:47,190
And so you'd say, that's
a second-order process.

519
00:26:47,190 --> 00:26:50,750
So again, you're determining
these things experimentally,

520
00:26:50,750 --> 00:26:53,390
collecting data,
plotting the data,

521
00:26:53,390 --> 00:26:55,880
determining rate
constants, determining

522
00:26:55,880 --> 00:26:57,165
the order of the reaction.

523
00:27:00,370 --> 00:27:04,260
Now, this is very exciting.

524
00:27:04,260 --> 00:27:08,270
What we're going to talk
about is the relationship

525
00:27:08,270 --> 00:27:12,830
between the rate constants
and equilibrium constants.

526
00:27:12,830 --> 00:27:13,590
So I love this.

527
00:27:13,590 --> 00:27:14,970
I love when we
come back to stuff

528
00:27:14,970 --> 00:27:17,100
that we've talked
about before and see it

529
00:27:17,100 --> 00:27:19,540
in a slightly different way.

530
00:27:19,540 --> 00:27:21,640
So at equilibrium,
we talked about how

531
00:27:21,640 --> 00:27:23,855
it's a dynamic process.

532
00:27:23,855 --> 00:27:25,730
And you have the rate
of the forward reaction

533
00:27:25,730 --> 00:27:27,370
equal the rate of
the reverse reaction.

534
00:27:27,370 --> 00:27:28,710
Reactions are still going.

535
00:27:28,710 --> 00:27:30,360
They haven't stopped.

536
00:27:30,360 --> 00:27:34,710
But the rates are equal
in both directions.

537
00:27:34,710 --> 00:27:38,380
So we've talked about how
to write an equilibrium

538
00:27:38,380 --> 00:27:40,550
constant for reaction.

539
00:27:40,550 --> 00:27:44,400
So if we have a reaction of
A plus B going to C plus D,

540
00:27:44,400 --> 00:27:48,960
we can write our equilibrium
constant k and its products

541
00:27:48,960 --> 00:27:50,780
over reactants.

542
00:27:50,780 --> 00:27:52,880
Unless one of our
products or reactants

543
00:27:52,880 --> 00:27:56,300
is a solid or a very
dilute solution.

544
00:27:56,300 --> 00:27:57,780
It's the solvent.

545
00:27:57,780 --> 00:28:01,030
And I heard from your TAs
that in the last problem set,

546
00:28:01,030 --> 00:28:05,690
some people had forgotten what
goes into q or k expressions.

547
00:28:05,690 --> 00:28:08,400
So it's good to review that for
this next unit and exam four

548
00:28:08,400 --> 00:28:12,810
and the final-- so
products over reactants.

549
00:28:12,810 --> 00:28:17,180
Now suppose we
tell you that it's

550
00:28:17,180 --> 00:28:21,500
a second-order process and the
rate of the forward reaction

551
00:28:21,500 --> 00:28:24,610
here, A plus B, we
can write the rate

552
00:28:24,610 --> 00:28:26,650
law for that forward
reaction being

553
00:28:26,650 --> 00:28:30,920
second order, first order
in A and first order in B.

554
00:28:30,920 --> 00:28:32,980
So the rate constant for
the forward direction

555
00:28:32,980 --> 00:28:37,130
is k 1 and then times the
concentration of A times

556
00:28:37,130 --> 00:28:39,430
the concentration of B.

557
00:28:39,430 --> 00:28:45,280
For the reverse reaction, the
rate constant is k minus 1.

558
00:28:45,280 --> 00:28:47,330
And this is generally
true in all the problems.

559
00:28:47,330 --> 00:28:52,710
If it's a first step, you have
plus 1 k1 on the top, k minus 1

560
00:28:52,710 --> 00:28:53,650
on the bottom.

561
00:28:53,650 --> 00:28:57,170
So we have k minus 1 times
the concentration of C and D

562
00:28:57,170 --> 00:29:00,970
So that's the
backward direction.

563
00:29:00,970 --> 00:29:06,360
So at equilibrium,
these rates are equal.

564
00:29:06,360 --> 00:29:07,460
We just talked about that.

565
00:29:07,460 --> 00:29:08,418
We've seen that before.

566
00:29:08,418 --> 00:29:10,580
The rate of the forward
reactions, so k1 times

567
00:29:10,580 --> 00:29:16,460
A times B is equal to k
minus 1 times C times D

568
00:29:16,460 --> 00:29:18,980
when you're at equilibrium.

569
00:29:18,980 --> 00:29:21,770
So we can rearrange
this equation now

570
00:29:21,770 --> 00:29:25,690
and say C and D over
here over divide

571
00:29:25,690 --> 00:29:31,560
by A and B. It's going to be
equal to k1 over k minus 1.

572
00:29:31,560 --> 00:29:35,490
And we also just saw that
C times D over A times B

573
00:29:35,490 --> 00:29:39,160
was equal to k.

574
00:29:39,160 --> 00:29:45,460
So therefore, our equilibrium
constant k equals k 1,

575
00:29:45,460 --> 00:29:49,630
the rate constant for
direction, over k minus 1,

576
00:29:49,630 --> 00:29:52,540
the rate constant for
the reversed direction.

577
00:29:52,540 --> 00:29:56,090
So here we're relating
equilibrium constants and rate

578
00:29:56,090 --> 00:29:58,160
constants.

579
00:29:58,160 --> 00:30:00,220
So we thought a lot
about what's true

580
00:30:00,220 --> 00:30:02,910
if you have a big
equilibrium constant.

581
00:30:02,910 --> 00:30:06,220
If you have a big
equilibrium constant,

582
00:30:06,220 --> 00:30:10,270
if you have an equilibrium
constant much greater than 1,

583
00:30:10,270 --> 00:30:13,530
what's the ratio of products
and reactants at equilibrium?

584
00:30:13,530 --> 00:30:17,390
Is there more or less products
at equilibrium and reactants?

585
00:30:17,390 --> 00:30:18,560
More.

586
00:30:18,560 --> 00:30:20,070
So we thought about
that, and now we

587
00:30:20,070 --> 00:30:23,380
can think about the relationship
of the rate constants.

588
00:30:23,380 --> 00:30:28,030
So if k is greater than 1,
is k 1 greater or less than k

589
00:30:28,030 --> 00:30:29,480
minus 1?

590
00:30:29,480 --> 00:30:31,270
Greater.

591
00:30:31,270 --> 00:30:34,030
And so that would
then be the case

592
00:30:34,030 --> 00:30:37,400
where you have more products
than reactants at equilibrium.

593
00:30:37,400 --> 00:30:39,530
If k is less than
1, a case where

594
00:30:39,530 --> 00:30:42,380
there's more reactants than
products at equilibrium,

595
00:30:42,380 --> 00:30:46,666
then you have k 1 is
less than k minus 1.

596
00:30:46,666 --> 00:30:48,040
So again, we can
think about this

597
00:30:48,040 --> 00:30:49,260
in terms of thermodynamics.

598
00:30:49,260 --> 00:30:53,620
We can also now think
about it in terms of rates.

599
00:30:53,620 --> 00:30:57,570
So one more thing that we need
to cover before we end today,

600
00:30:57,570 --> 00:31:02,300
and that is about elementary
steps and molecularity,

601
00:31:02,300 --> 00:31:04,910
which I just love
saying that word.

602
00:31:04,910 --> 00:31:06,400
So on Monday,
we're going to talk

603
00:31:06,400 --> 00:31:08,110
about mechanism of reactions.

604
00:31:08,110 --> 00:31:10,587
Most reactions do not
occur in one step,

605
00:31:10,587 --> 00:31:12,170
and we need to think
about mechanisms.

606
00:31:12,170 --> 00:31:12,730
I said it was Wednesday.

607
00:31:12,730 --> 00:31:13,820
But it's actually Monday.

608
00:31:13,820 --> 00:31:14,690
So it's coming up.

609
00:31:14,690 --> 00:31:15,884
It's very exciting.

610
00:31:15,884 --> 00:31:18,050
And we're going to talk a
lot about elementary steps

611
00:31:18,050 --> 00:31:19,960
when we talk about mechanisms.

612
00:31:19,960 --> 00:31:26,530
So an elementary step is one
of the steps in the reaction.

613
00:31:26,530 --> 00:31:28,520
So reactions usually
don't occur in one step.

614
00:31:28,520 --> 00:31:30,800
They have many
steps, and each step

615
00:31:30,800 --> 00:31:33,970
is called an
elementary reaction.

616
00:31:33,970 --> 00:31:38,870
So we talked about last time
that for the overall order

617
00:31:38,870 --> 00:31:41,340
of the reaction, you can't
just look at the stoichiometry

618
00:31:41,340 --> 00:31:43,610
and say what the order
of the reaction is.

619
00:31:43,610 --> 00:31:46,100
So you can't predict
it from stoichiometry

620
00:31:46,100 --> 00:31:48,020
for an overall reaction.

621
00:31:48,020 --> 00:31:52,720
But if it's an elementary
reaction, if it's a step,

622
00:31:52,720 --> 00:31:57,970
that elementary reaction is
written exactly as it occurs.

623
00:31:57,970 --> 00:32:02,760
So in that case, the order and
the rate law can be predicted.

624
00:32:02,760 --> 00:32:04,200
So this is you're
breaking it down

625
00:32:04,200 --> 00:32:07,120
into sort of the smallest
unit, the smallest

626
00:32:07,120 --> 00:32:10,550
step, this elementary
reaction, so you can just

627
00:32:10,550 --> 00:32:13,530
look at the stoichiometry
for a single step,

628
00:32:13,530 --> 00:32:16,180
for an elementary
reaction, and project

629
00:32:16,180 --> 00:32:19,190
to the order and the rate law.

630
00:32:19,190 --> 00:32:22,699
So elementary reactions
occur exactly as written.

631
00:32:22,699 --> 00:32:24,490
So that's what we're
going to do on Monday.

632
00:32:24,490 --> 00:32:27,080
We're going to break
down our mechanisms

633
00:32:27,080 --> 00:32:29,800
into elementary steps,
write out the rate laws,

634
00:32:29,800 --> 00:32:34,610
and then figure out what kind
of mechanism we might have.

635
00:32:34,610 --> 00:32:39,750
So finally, molecularity--
so molecularity

636
00:32:39,750 --> 00:32:43,240
is just the number of
things that come together

637
00:32:43,240 --> 00:32:45,960
to form a product.

638
00:32:45,960 --> 00:32:53,310
And here we have three names--
unimolecular, bimolecular,

639
00:32:53,310 --> 00:32:54,990
and termolecular.

640
00:32:54,990 --> 00:32:57,040
Unimolecular process,
what do you guess?

641
00:32:57,040 --> 00:33:00,150
How many reactants are coming
together to form product?

642
00:33:00,150 --> 00:33:02,380
One.

643
00:33:02,380 --> 00:33:04,580
Bimolecular, what do you guess?

644
00:33:04,580 --> 00:33:05,740
Two.

645
00:33:05,740 --> 00:33:09,390
Termolecular is a little harder,
but just give it a whirl.

646
00:33:09,390 --> 00:33:10,910
Three, yes.

647
00:33:10,910 --> 00:33:13,700
So bimolecular is very common.

648
00:33:17,490 --> 00:33:19,740
And termolecular is not.

649
00:33:19,740 --> 00:33:23,220
So I have three molecules
to come together.

650
00:33:23,220 --> 00:33:24,690
And if you try to
think about how

651
00:33:24,690 --> 00:33:27,980
you get three things to come
together all at the same time,

652
00:33:27,980 --> 00:33:28,910
that's kind of rare.

653
00:33:28,910 --> 00:33:30,990
Usually, when there are
three things reacting,

654
00:33:30,990 --> 00:33:32,470
there are multiple
steps involved.

655
00:33:32,470 --> 00:33:33,870
But two is good.

656
00:33:33,870 --> 00:33:37,840
Now finally, we'll end
with a clicker question.

657
00:33:37,840 --> 00:33:40,080
Think about which of
these would be examples

658
00:33:40,080 --> 00:33:41,671
of unimolecular processes.

659
00:33:52,820 --> 00:33:53,476
10 seconds.

660
00:34:08,719 --> 00:34:11,120
So it actually is one and two.

661
00:34:11,120 --> 00:34:14,100
So most people got the two.

662
00:34:14,100 --> 00:34:16,290
Yes, that's radioactive decay.

663
00:34:16,290 --> 00:34:18,909
But the other, you can
have a decomposition.

664
00:34:18,909 --> 00:34:21,960
So here we have decomposition
into its elements

665
00:34:21,960 --> 00:34:26,060
is also a first-order process.

666
00:34:26,060 --> 00:34:27,500
Happy Thanksgiving, everybody.

667
00:34:27,500 --> 00:34:29,859
See you next Monday.