Scale of the small | Scale of the universe | Cosmology & Astronomy | Khan Academy

What I want to do
in this video is explore what happens when we
get to really, really, really small scales. And before we even
think about it, I want to familiarize
ourselves with the units here. So, we’re all familiar with
what a meter looks like. The average adult male is
a little under two meters. If you were to divide a
meter into 1,000 units, you would get a millimeter. And I think we probably
know what a millimeter is. If you’ve ever looked
at a meter stick, it’s the smallest measurement
on that meter stick. So it’s already pretty
hard to look at. Now, if you were to divide
each of those millimeters into 1,000 sections,
you’d get a micrometer. Or another way to think
about a micrometer is, it’s one
millionth of a meter. So this is kind of
beyond what we’re capable of really perceiving. If you were to take each
of those micrometers and divide them
into 1,000 sections, you would get a nanometer. So now we’re at one
billionth of a meter. You divide that by 1,000,
you get a picometer. So a picometer is 1,000
billionth of a meter, or you could say a
trillionth of a meter. You divide one of
those by 1,000, and you would get a femtometer. So these are unimaginably
small things. Now once you’re
familiar with the units, let’s explore what
types of things we can expect to find at
these different scales. And I’ll start over here. And I’ve written them
on the left as well, but it’s more compelling
when you see the pictures. We’ll start over
here with the bee. And I’ve arbitrarily picked
something of this scale. There’s many, many, many,
almost an infinite number of things I could have
picked at this scale. But the average bee is
about two centimeters long. This bee right over here. It’s about, give or take, it’s
about one hundredth the length of the average
adult human being. But once again,
the honey bee not too exciting, although
it is pretty exciting to see it zoomed in like this. But a honey bee is something
that we can relate to. We’ve all seen honey bees. Now, what I want
to do is zoom in, or look at something that’s 50
times smaller than a honey bee. So something that if I
were to show how big it is relative to this honey
bee, it would look something like this. I’m doing it very rough. And that is a dust mite. And this right here, these are
both pictures of dust mites. Now dust mites look like these
strange and alien creatures, but what’s amazing about them
is that they are everywhere. They’re all around us. You probably have many of them
lying on your skin or wherever right now, which is
kind of a creepy idea. But we’re talking
about scale here, and the average
dust mite– so we were talking about
centimeters before, now we’ll talk about
millimeters– the average dust mite is less than
1/2 of a millimeter. Or if you want to
talk in micrometers, it’s about 400 micrometers long. So this length right over
here is about 400 micrometers, so about 1/50th the length–
remember, this huge thing that I’m showing right
here, this is a honey bee. It’s about 1/50th of the
length of the honey bee. Or maybe to put
it in other terms that you might be
familiar with, this is a zoomed-in
picture of human hair. And you might say, oh my god,
this person has horrible hair, but no. If you looked at your own hair
under an electron microscope, you’d be lucky if
it looked this good. This person, actually I’ve seen
pictures of more damaged hair than this. This is probably smooth
and silky hair right here. But the diameter of human
hair, and this is on average, it depends on whose hair
you’re talking about, the diameter of human
hair is about 100– you can’t see it when
I write in that color. It’s about 100
micrometers thick. That’s the diameter. So it’s about a fourth
the length of a dust mite. Or if I were to draw some human
hair relative to this honey bee, it would look
something like this. It would be about– and I’m
drawing the whole hair– so its width would be the width
of this thing that I just drew. Now remember, we’re looking
at a honey bee here. It looks like some type of
giant, but it is a honeybee. Let’s zoom in even more. So, we started
with the honey bee. We zoomed in by 50
to get the dust mite. We zoomed in by
another factor of 4 to get the width of human hair. If we zoom in, we’re in
the micrometer range now. If we zoom in by another,
roughly, another factor of 10, we get to the scale of cells. And this right here
is a red blood cell. I think this is a white
blood cell right over here. About 6 to 8 micrometers. So once again, if I
were to draw a cell relative to this human
hair, it would probably look something like this. Something on a similar
scale that we can still kind of relate to, is
the width of spider silk. It’s about 3 to 8 micrometers. So if I were to draw some
spider silk on the same diagram, it would look
something like this. This is an actual
image of spider silk. So, once again, something
that we can kind of perceive. You can bump into it, you
can touch spider silk, you can see it if the sun
is reflecting just right, or if it has a little
bit of moisture on it. But it’s about the thinnest
thing that humans can perceive. And this is in the ones
of micrometer range. At that same range,
you start to have some of your larger bacteria. Bacteria can be
anywhere from– and I’m speaking very roughly–
1 to 10 micrometers. So in general, they’re
smaller than cells. Most bacteria are
smaller than most cells. And just to figure out
where we sit on our scale, I have it over here. So we started off–
I want to keep reminding ourselves– humans. You divide by 100,
you get to the bee. So each of these slashes
right here are dividing by 10. So this is divide by 10. Divide by 10 again, you’re
divided in size by 100. Divide by 10 again,
you get to millimeter. You’ve divided by 1,000. Divide by 10 again,
you are doing tenths of millimeters,
which is about the size of the human hair. You divide again by 10, you’re
going to tens of micrometers. By 10 again, you get into
the micrometer range. So now we’re talking about
human hair– not human hair. Human hair we did up here. We’re talking about cells. We’re talking about bacteria. Now things are going
to get really crazy. Now they’re going to get
really, really, really crazy. This was in the ones
of micrometer range. Now we’re going to start getting
into the hundreds of nanometer range. And just to get a
sense of things– So remember, a nanometer is
a thousandth of a micrometer, or 100 nanometers would be
a tenth of a micrometer. And this picture right here,
this big enormous planet or asteroid looking thing,
this is a white blood cell. The enormous blue
thing in this picture. And so if I were to zoom out,
it would might look something like this right over here. But what’s really fascinating
about this picture for multiple reasons are
these little green things that are emerging after
essentially reproducing, emerging from the surface
of this white blood cell. And these things right here,
these are AIDS viruses. So now if we zoom in roughly
another factor of, you know, about 100 to 1,000 from
the size of a cell, you are now getting to
the size of a virus. And all of the genetic material
necessary to replicate that virus is right inside each
of these little capsids. It’s right inside each of
these little green containers. So now, going back
to our scale– let me get my scale
right over here– we are down to the
scale of a virus. So we’re in the hundreds
of nanometer range. If we divide by 10
and then divide by 10, you get to the nanometer range. And right in the ones
of nanometer range, you get to the width of the
double helix of a DNA molecule. So this right here is,
if you were to zoom in, and this is an artist’s
depiction of it, obviously. Well, this is not a picture,
so to speak, of a DNA molecule. But the width of this double
helix is about 2 nanometers. Or another way to
think about it, about 1/60th the diameter of
one of these viral capsids. Which it would have
to be, because it’s going to have to
get all wound up and fit into one of
these viral capsids. And DNA, just to make it clear,
this is just the width of DNA. It’s much, much, much, much,
much, much, much, much longer. And we can talk about
that in future videos. So once again, we’re at
a very, very small scale. If you want to think of
it in terms of meters, we’re at two
billionths of a meter. You could put 500
million of these side by side to get to a meter. Or you could even
think of it this way, this is two millionths
of a millimeter. So once again, super small. You could put these side by
side, one DNA, and another DNA, and if you made them touch,
you could put 500,000 next to each other
in a millimeter. So this is unbelievably
small amount of space. And now I’ll introduce
you to another unit that’s not kind of in the
conventional, you know, prefix followed by meters. And this is an angstrom. And 10 angstroms
equal one nanometer. So the width of this
DNA double helix, it would be two nanometers
or 20 angstroms. Now, if we were to
divide again by 10, you get to something that’s
2 angstroms or 0.2 nanometers wide, and that is
a water molecule. Maybe instead of
using red, I should have used blue or something. But this right
here is the oxygen, and it is bonded to the 2
hydrogens right over here. So we’re getting,
you know, this is beyond, frankly, human
perception, I mean. Or even really, stuff
that we can conceptualize. Not to even speak
of perception, I have trouble imagining
how small we’re dealing with right over here. We’re essentially
dealing, remember, we’re dealing with less, 1/5
of a billionth of a meter, or 1/5 of a millionth
of a millimeter. Something that I
really can’t fathom. But we’re going to get
even smaller than that. If we were to zoom in on one
of these hydrogen atoms– and now things start to
get kind of abstract, and we start dealing
in the quantum realm. And it’s hard to define where
one thing ends and one thing begins. And what is real? And what is not real? And all of that silliness. But if we try our best to
do it, if we were to zoom in and we sort of put some
boundary on a hydrogen atom– because electrons actually
could jump around anywhere– but if we set some boundary of
where the electrons are most likely to be found, the
diameter of a hydrogen atom is roughly 1 angstrom. Which makes sense from
this diagram, too. It’s about 1/2 of the diameter
of this water molecule. What’s extra crazy
is one, this atom is super, super duper small. Something that we
can’t, you know, this is one ten
billionth of a meter, or one ten millionth
of a millimeter. So something we really,
really can’t fathom. But what’s crazier than that,
is that it’s mostly free space. We’ve gotten this
small, we’re trying to get to these
fundamental units, and this thing right here
is mostly free space. And that’s because if
you look at an electron, and when we say
radius here, it’s really hard to define
where it starts and ends. And you have to do some
things related to the charge. And we’re not even thinking
about quantum effects and all of that. An electron has a
radius of 3 times 10 to the negative 1/5 angstroms. And the nucleus of
a hydrogen atom, which is really just a proton,
has a radius a little bit– and you don’t even worry
about this number right here. The general idea is, it’s
the same order of magnitude. It’s about 1/10,000th
of an angstrom. And just to give a
sense of what it’s like, if you have the entire, if you
view the entire atomic radius to be about an
angstrom, kind of, just have a conception
for scale of the atom and how much free space
there is in an atom, if we even want to think
what is free space. Imagine a nucleus
being maybe a marble at the center of a
football stadium, of a domed football stadium. And imagine an electron being a
honey bee just randomly jumping around random parts
of that entire volume inside of that football stadium. And obviously, it’s
a quantum honey bee, so it can jump around
from spot to spot, and it’s not easy
to predict where it’s going to go next,
and all of the rest. But that will give you
a sense of the scale of the electron and the
proton relative to the atom as a whole. But even more
crazy, it gives you a sense for how empty atoms,
and really all matter really is.


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