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[MUSIC]

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Hi, and welcome to this in-depth extra
lecture on week one, your not going to

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see my picture in this lecture, cause I
want you to watch what I write.

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We're going to be going over five topics
in the next probably 20 minutes.

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We're going to be converting among size

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unit, estimating the numbers of things,
the surface

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area of things, the size of things,and
finally

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I'll talk about an atoms in a cluster.

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There's a companion worksheet that you can
use.

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That will provide some written material
that hopefully will

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reinforce what we're going to be doing in
the next couple of slides.

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Unlike our primary lectures, this resource
is really

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provided to allow you to do well on the

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in-depth quiz and also to see some problem
solving

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if you have some questions about how to
tackle.

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The quantitative part of the class.

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Okay, so let's start with this first
example.

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I'll let you go ahead and read that.

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my advice is to go ahead and try to solve
this problem yourself, and then

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watch how I do it.

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Okay, so in this question you had to think
a little

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bit about the geometry, because what
you're being asked to do.

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Is to cut kind of like a bologna slicer,
for a piece of silicone

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that's something like this in shape, so
your going to be cutting,

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nanometer thick pieces of these AFM probes
and the probes

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themselves are 35 nanometers.
In their thin width.

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So, if you weren't sure how to do this
problem, odds

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are it had something to do with getting
this geometry right.

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But if we go ahead and say what this
problem is really asking us is how

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many, so that can often be the more

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complicated thing, is just to get to that
point.

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So let me show you how we set this up.

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We always write down what we're given,
we're given the centimeter.

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And this is a conversion problem.
We know that one centimeter, is 10 to the

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minus 2 meters.
We know that one meter is equal

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to 10 to the positive 9 nanometers.
And now what we want to know

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is.
35 nano meters is equal to 1 probe.

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So we're assuming we have plenty of width
and length to deal

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with and when we multiply all that out
what we're going to find.

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Is 2.9 times 10 to the positive 7 times 10
to the minus 2.

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Or on the order of 3 times 10 to the 5.
And that's

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300,000 tips.

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And a tip in this case is equal to a
probe.

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Now what's also important to realize is a
step I did right here.

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When you know that you have something
that's equal, like one

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probe, you can rewrite that as one probe.

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Over 35 nanometers.
And that is equal to one.

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So it's part of a unit conversion.

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It's just telling us if we want to go from
nanometers to probes, that's how we do it.

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Now the other thing that I was doing that
I just want to point out explicitly.

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So I was also cancelling units.

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So if you're wondering how did I know to
put centimeters on

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the bottom, and meters on the top, it was
a unit cancellation trick.

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Now, let me go ahead and give you a

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hint on this next example, which is on
your quiz.

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In this example, it's just like what we're
doing

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here, except now you have a four
centimeter post-it note.

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And I'm asking you to figure out.

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How many carbon nanotubes, if you laid
them flat down, would fit?

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So it's very similar to the example that
we just did.

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Okay, let's go on to the next slide.

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So in this example, we're going to be
calculating finding the number of objects.

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And the first thing that I want to

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remind you is that this problem specifies
spherical particles.

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So what that means is that the volume of a
single particle is going to be 4 3rds pi.

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R cubed.

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That's just a basic geometrical fact for r
spheres.

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And how we're

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going to do this is we're going to start
by calculating the volume of one particle

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and I'm going to call that a nanoparticle,
so this is equal to np

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for nanoparticle.
This is just going to be 4 3rds.

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Pi, now R in this case remember, is 2.5
nanometers and I'm going to cube that, the

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next thing I'm going to do is realize I'm
going to want all my units in centimeters.

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So what we do is we write that conversion
but we cube it, because

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this a nanometer cubed so that has to be
nanometer cubed to get centimeters cubed.

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So when we multiply all of that out what
we're going to get is 6.5.

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Times 10 to the minus 20.

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And that makes sense because we only have

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a single nanoparticle, so it should be
very small.

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I also want to estimate that, sorry.

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I also want to point out that what we're
doing here is we're really, estimating.

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So I'm not going to be paying close
attention to

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things like significant figures or where
the decimal point is.

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That would be something I would do in a
formal class.

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That was, for example, a whole semester,
but I'm just

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trying to give you the basics of how to
approach this.

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Okay, so that's the volume of a single
nano particle.

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Now the next piece of information we have
then.

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Is, we were given 10 microliters for our
injection

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capacity, and that just comes from the
problem itself, there.

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So we're going to shift, to centimeter
cubed.

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Now what we're going to do is divide by
the volume of a single particle.

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And here's how we write that.

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I know the single particle is 6.5 times 10
to the minus 20.

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Cenitmeter cubed and that is one nano
particle.

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So when I multiply all of this out,

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what I find.

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And again these are estimates I'm not
carrying that 1.5 and I'll go ahead

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and finish cancelling my unit so again
this term right here is an important

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one because its saying the volume in a
single nano particle and this is

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how you go from volume to the numbers of
particles is by figuring out.

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The volume of a single nanoparticle, I get
a way to get rid of centimeter cubed, and

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introduce nanoparticles as a unit.

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Okay, this last one is going to be very
similar.

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for this objects discussed, how many of
these particles would weigh one gram?

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So in this case, you do need to know the
density.

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So you're going to start with the one
gram.

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So hint,

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start with one gram,

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take that to volume,

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and then use the conversion above.

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So you can use the same of one
nanoparticle is equal

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to about 6 times 10 to the minus 20
centimeter cubed,

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so your going to end up dividing just like
you did here,

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but all of the work here will be a little
bit different.

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Okay let's go on to the next problem.

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So again I just want to make the point
that we're estimating.

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Just so we don't have to be quite

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as careful with all the little details,
and let's

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think about this, so now we doing surface
areas,

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so that's going to be a little bit
different.

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We talked about that in lecture and so the

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two pieces of data that I'm going to give
you.

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Is that you can have a cube, and

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then the surface area of the cube is,
there

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are six spaces to the cube, and the area

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of each face is 2 times R, where R is just
half the size of a face, squared.

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If you have a sphere.

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The surface area its just 4 pi R squared.
So in this problem

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I ask you to consider both spheres and
cubes just to give you some practice.

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Okay, so let's get started.

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So in this problem, just like before, one
of our

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first things we're going to do is,
calculate the volume

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of the nanoparticle, because we're going
to need to know

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how many nanoparticles that we actually
have in this entire situation.

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So, funnily enough, if you use a cube,
then the volume of the cube, of

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course is just going to be.
2R cubed.

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And if you have a sphere, the volume of a
sphere is just 4 3rds pi r cubed.

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So I'm going to go ahead and calculate
this out, just for kicks, as a cube.

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So I'm going to start with 2 r cubed.

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That's going to equal to 8, so that's
going to be 5 nanometers radius.

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I could have just left that, but I didn't.

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Remember I'm going to want everything in
centimeters cubed, so I already know.

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That, I'm going to use this conversion.
And

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when I work all that out, I get something
like this.

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Now the other thing I'm going to have to
do is the surface area.

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Of a nano-particle.

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That's just going to be equal, assuming
also I have cube again.

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To 6 times the edge length

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squared.
So that's going to give me 2 times

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2 is 4, times 6 is 24, times 5 nanometers.

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Squared.

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Now, I'm going to have to go from seven to
get to centimeters.

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And that's just going to be squared.

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So I have a slightly different conversion.
Well what I get for all of this is 6

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times 10 to the minus 14 centimeters
squared.

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So putting all that together then, I'm
going to take one gram.

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I'm going to convert that to volume
through my density,

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remember that density let's us go from
weight to volume.

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And you can see the density number right

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there, and that's exactly what I used
here.

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I also know I'm writing gm sometimes,
really

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to be accurate I should be writing g.

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But I have a bad habit of writing gm, it's
the same as g, or grams.

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Okay, so that gives me the volume.

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Now

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I'm going to go one particle.

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So what I'm figuring out here in this part

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of the calculation is, how many particles
are there?

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So you always have to figure out how

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many particles in these calculations to
start off with.

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So now we have.

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If we stopped, we'd have the number of
particles.

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Okay, but what I care about is the surface
area of all of these.

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So, I'm going to go back and

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use this number and I'm going to say,
okay, that's how many particles I have.

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And I know for every particle, I have this

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much surface area, and when I put all that

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together I get something on the order of,

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100,000 centimeters squared.

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Which is a whole lot of surface area

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that's like 10 meters squared so that's a
lot.

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Now I went ahead and did this for a

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sphere which means I used this number and
this number.

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And I did get something too different if I
used, if I did this for spheres.

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I got something that look like to be about
60 meters squared.

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So it's about an order of magnitude
difference.

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If you take a sphere versus a cube.

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Now on this last problem which is one of
your

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quiz problems, it's really similar to what
I just did.

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You're going to start.

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By taking the 500 milligrams, you're
going to convert

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that to volume using the density of gold.

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Then you're going to do the same thing,
you're going to get number of particles,

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and then you're going to get total surface
area.

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And remember when you shrink, the particle
diameter.

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From 1.15 to 1.5.

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That's an order of magnitude.

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So you should increase your surface about
an order of magnitude.

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Okay.

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Let's go to the next slide.
Okay.

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So this is pretty simple but I was just
going to go over

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it in case anyone had any questions based
on my size of things lectures.

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So this is also very much related to the
nanoworld lecture.

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As well

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as the demo.

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So when I did the demo, I sort of assumed

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if I was 10 nanometers, how big would
things be?

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So it's kind of a strange question, but
I'm about five foot six.

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So 1.65 meters, in my world, and I was
writing kind of

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the big world.
Is equal to one nanometer in the small.

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So in this example, we're not doing 10
nanometers, we're doing

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one nanometer.

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So that's what's a little bit different
than the lectures.

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And we're given a molecule, naphthalene,
and we're told it's five angstroms.

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So I'm going to start with that.

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So five angstroms, there's the symbol for
angstroms.

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I knew that one angstrom is actually, I'm
going to

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take a jump here, it's a tenth of a
nanometer.

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And so it's an aromatic hydrocarbon, and

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it's about 0.5 nanometers, roughly, in
this dimension.

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Or five angstroms.

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Okay so what I'm going to do is I'm going
to take this and I'm going to say this is

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how big it is in the small world, in the
kind of world that it exists in so one

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nanometers in the small world, so you go
to 1.56 meters.

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In the big world.

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Anyhow, if you work that out, what you can
figure out is that

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naphthalene is going to be about, half
1.65 meters, or half my height.

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So I need something that's about half my
height.

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So I like a chair, about half my height or
kind of

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more like the naphthalene because its a
plainer molecule, maybe a large kite.

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00:15:11,360 --> 00:15:14,590
So that's kind of how to think about it,
what you do is once your one nanometer

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you sort of say is the object half my
size, twice my size, 10 times my size?

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You can usually get there, but this is how
to do the math if you want to see it.

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So this problem is pretty similar, you're
still one nanometer.

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00:15:24,650 --> 00:15:31,070
So I would take the three nanometers.
So whatever this is, it's

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gotta be three times, taller than me.

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Or you.

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00:15:38,800 --> 00:15:42,220
So you have to pick objects that are about
three times taller than you because

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you are one nanometer so if it's three
times taller you got to think about it.

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Okay lets go to the very last slide.

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So this is actually some advanced work
that I just wanted

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to give those students who were really,
really wanting to push themselves.

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And what I wanted to do is actually
recognize that in a nanocrystal,

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you saw that picture of Cadmium Selenide
with all the little dots?

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They're actually atoms.

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00:16:10,290 --> 00:16:13,900
And so in a crystalite that's three
nanometers.

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In diameter, there's going to be hundreds
of atoms inside of it.

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So how do you calculate how many atoms are
held in a nanocrystal?

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So, it's kind of interesting.

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You have to realize,

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that one of these atoms.
Which is, let's say in

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this case, a gold atom.
A single atom weighs its atomic

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00:16:38,355 --> 00:16:43,395
number times the atomic mass unit which is
just a fixed

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unit which is 1.6.
going to take 1.66

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00:16:48,518 --> 00:16:53,306
times 10 to the minus 24 grams

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per kind of atom.

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So, if you work this out, you can figure
out how much a gold atom weighs, and then

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00:16:59,092 --> 00:17:00,831
if you know how much the whole thing
weighs,

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you can figure out how many gold atoms are
there.

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00:17:02,990 --> 00:17:04,820
So that's going to be our strategy.

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00:17:04,820 --> 00:17:11,028
So, let me get started.
So we know that the volume is equal to 4

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00:17:11,028 --> 00:17:18,420
3rds pi.
1.5 nanometers cubed times 10 to

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00:17:18,420 --> 00:17:23,290
the minus 21 centimeter cubed per
nanometer cubed.

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00:17:24,560 --> 00:17:27,940
All of that gives us 1.41 times 10 to the
minus 20 centimeter cubed.

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I'm going to multiply that by the density.

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00:17:34,050 --> 00:17:35,600
And I'm going to get a weight.

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00:17:40,020 --> 00:17:42,130
And this weight is going to be the weight
of a gold particle.

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00:17:43,510 --> 00:17:51,280
And so then, I'm going to divide the
weight, of one nanoparticle.

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By, 200 times 1.66 times 10 to the

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00:18:00,456 --> 00:18:06,300
minus 24 grams per atom.
So let me show you how this works out.

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So four thirds pi R cubed, multiplied by
10 to

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00:18:11,500 --> 00:18:16,560
the minus 21.
Centimeters

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00:18:16,560 --> 00:18:21,540
cubed per nanometers cubed times 19.3
grams

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00:18:21,540 --> 00:18:23,150
per centimeters cubed.

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00:18:23,150 --> 00:18:26,040
Now we're onto weight of the entire
particle.

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00:18:26,040 --> 00:18:28,630
And I know that I have one gold atom

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00:18:30,930 --> 00:18:39,800
and it weighs 200 times 1.66 times 10 to
the minus 24 grams.

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00:18:39,800 --> 00:18:42,150
And going ahead and just doing my unit
analysis.

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00:18:43,518 --> 00:18:47,320
This is going to kill that, there's my
centimeters go away, grams go away, and

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00:18:47,320 --> 00:18:49,720
I'm going to get the number of gold atoms,
which is what I want.

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00:18:49,720 --> 00:18:52,200
And when I work all that out, I get
something on the

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00:18:52,200 --> 00:18:55,760
order of 820, which I like very much
because that's, I know,

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00:18:55,760 --> 00:18:56,880
about the right answer.

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00:18:56,880 --> 00:18:58,610
Now, my hint on this last question,

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because this a question on your in-depth
quiz.

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00:19:02,530 --> 00:19:05,800
You're just going to do the reverse.
You're going to take 66 gold atoms.

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00:19:09,530 --> 00:19:15,170
You're going to figure out the weight.
You're going to figure out the volume.

289
00:19:15,170 --> 00:19:18,000
You're going to get the radius.

290
00:19:18,000 --> 00:19:20,960
You're going to have to take a cube root
to do that.

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00:19:20,960 --> 00:19:23,170
And then, you're going to double to get
the diameter.

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00:19:25,670 --> 00:19:28,010
So, have fun with that, and you know from
this

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00:19:28,010 --> 00:19:30,870
answer it better be a lot smaller than
that one.

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00:19:30,870 --> 00:19:33,680
I hope this has been useful for those of
you who are trying to do the in-depth.

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00:19:33,680 --> 00:19:36,410
I just wanted to do some of our
quantitative problem solving.

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Please go ahead and try the in-depth quiz.
You get five tries on these questions.