Atoms: The building blocks of everything around you. That atoms are extremely small probably
isn’t something I have to tell you - But how small exactly are they? That’s where
things get a bit more interesting, because that’s actually quite difficult to answer
visually. Now of course I could tell you that a carbon
atom has a diameter of only 1.4E-7 mm, but that would hardly help you to visualize the
scale of atoms – such a value is simply too abstract. Similarly I could say that 1m²
of Diamond would contain about 1.75*10^29 atoms, but that too wouldn’t necessarily
bring us any closer to a clear picture of how small atoms really are.
To illustrate the scale of atoms properly we have to bring it in a context that is still
somewhat visualizable. And that’s exactly what we will be attempting to do today. Because
the tiny dimensions we’re talking about make this not at all easy, we will explore
three different approaches at once, so that at by the end hopefully everyone has a better
understanding of how small atoms really are. Before we begin lets quickly establish how
big a millimetre is, for our American audience because inches are way too big for the task
at hand. If we take a look at this ruler than this is an inch, and this is a millimetre.
So a millimetre is almost exactly 1/25th of an inch, or based on this ruler: 2/3rds of
1/16th. So when I say something like 1/5th of a millimetre than that’s 1/5th of this
blue area. Great, let’s begin. One of the smallest things visible to the
naked eye is a human hair. This makes it the perfect starting point. On the one hand it’s
so small that the numbers don’t instantly explode into absurdity but on the other hand
everybody should have a clear understanding of its dimensions.
Now of course hairs vary in thickness (little black curly hair) but your average head hair
is about 1/10 of a millimetre thick. Atoms also don’t have a uniform scale. Their Size
varies depending on the element, the chemical environment and even how they are arranged.
Our model of the atom simply is just that, a model. As much as we like Atoms to be perfectly
defined marbles, in reality it’s not that simple. However, to make this video we have
to use some figure: For a carbon atom, the third most common atom in our body, 140 picometers
is, I think, a fair value: That’s roughly 1/7.000.000th of a millimetre. That means
a human hair is on average as thick as a strand of 700 000 carbon atoms, which showcases quite
well how small atoms must be. But 700.000 too isn’t necessarily a conceivable
number especially on the inside of a human hair. So what if we scaled up each of these
atoms, but only to the point that each atom itself has the diameter of a human hair and
would therefore barely be visible to the naked eye. If we did that the hair would be an astonishing
70meters or 230 ft thick - almost as tall as the Big Ben in London.
But these 700.000 Atoms of course only form a one dimensional string 1/7.000.000th of
a millimetre thick. To fully appreciate how numerous and therefore small atoms are we
have to explore all three dimensions. So let’s continue with an area. What if
we covered the cross section of a hair with a layer of carbon atoms? That’s calculated
easy enough. If we plug the radius of 350.000 atoms in the formula for the area of a circle
we get an area of 390.000.000.000 (390 billion) atoms. Roughly that many carbon atoms fit
on the cross section of a hair. Why is this number important? As mentioned
earlier, objects 0.1mm wide (so the width of a human hair) are just distinguishable
by good eyes. That means the cross section of a human hair is the smallest point you
can still make out with your own eyes and thus an area of 390 billion carbon atoms is
the smallest area of atoms visible to the naked eye, at least theoretically. Because
while a monolayer of carbon atoms does absorb around 2-3% of white light making it ever
so slightly opaque, such a small dot would probably still be too transparent to be distinguishable
without a few more layers of atoms below it. Still, If you put the end of a cut hair between
your fingers and press your fingers together so that only the very tip peeks out, on this
tiny point would fit roughly 390 billion carbon atoms - an inconceivably large number.
To put this number into perspective lets go back to our scale up from earlier. But this
time picture it as a giant 70m or 230ft thick paint brush made from human hair tightly backed
together with no room in between. Humans have around 100.000 hairs on their head, so for
a paintbrush that size would need to sheer the heads of around 4.000.000 people.
If each of these hairs would represent one atom then that’s how many carbon atoms would
fit on the tip of one of your hairs. And this is just a single layer of atoms.
There is still one dimension left to explore and that’s where the numbers really become
mind bogglingly large. But for that task we should probably switch to an object that is
a little easier to see in detail, which brings us to our second approach.
This time lets use a grain of Sand. The average grain of sand has is about half a millimetre
big, so about 5-times the diameter of a hair. Technically speaking sand isn’t made up
of a particular material as it is only defined by size of its particles. It is finer than
gravel but coarser than silt. Typically however Sand of course composed of Silicon dioxide
so quartz. Our grain of sand would weigh about 200 micrograms.
Using the molar mass of silicon dioxide we can calculate that there are around 10^22
molecules in a gram of sand. Since each molecule of silicon dioxide contains 3 atoms this amounts
to 6*10^18 or 6 quintillion atoms in our grain of sand.
Using our trick from earlier and scaling up each of these atoms to the size of a grain
of sand our grain would be roughly 1100m or 3600ft tall, 3 times as tall as the Empire
State Building. Or to put it differently: If you’d cover
an area of 750 km² - roughly the size of New York City – with a layer of sand up
to your belly button, you would have about as many grains of sand in that layer as there
are atoms in a single grain. Granted that’s not nearly as many atoms
as there are grains of sand on the entire planet, as some trivia sites claim but it’s
still an absurdly large number that gives you a good understanding of how small atoms
really are.
The final approach we want to explore is arguably the most abstract one, but it’s also the
most fun one. How many atoms are in your body? Given that
a single grain of sand already contains quintillions of atoms it doesn’t really make sense to
try to visualize the number in a conventional way. Instead let’s try something a little
different. What if we made a human sausage? What if we
put a human (obviously a very bad one, like a murderer or a lawyer) through a meat grinder
and then rolled him out thinner and thinner and thinner. How long could that sausage get?
How long could a single human theoretically get?
The first step would be to roll him out so thinly that we end up with a string of individual
cells. How long would such a human cell thread be?
How many cells there are in a human body can of course only be estimated and even that
is harder than it seems. For a start, the cells in our body differ vastly in size. Red
Blood cells for instance a teeny tiny, only 1/150th of a millimetre wide. Sperm cells,
the smallest cells in our body are even smaller. On the other side of the spectrum we have
fat cells for instance, with a volume roughly 20.000 times larger. The largest cells the
female egg cells are so large they are even visible to the naked eye. On top of that,
the different cells also vary significantly in density.
All this makes an accurate estimation of the amount of cells in our body quite challenging.
By dividing the body into its individual organs and parts and those again into their cell-types
scientists in 2013 for the first time made an attempt at a more accurate estimation.
Their result: The body of an average human not including the countless bacteria and microbes
that live within us contains roughly 37 trillion (3.72*10^13) cells.
If we assume that an average cell has a diameter of 1/50th of a millimetre, then a string of
all those cells would have a length of 740.000 km – 460.000 mi and would reach 18 times
around the world. Now let’s break each of these cells down
into its individual atoms – How long would the human body then be.
Earlier we learned that you could fit 390 billion carbon atoms on the tip of a hair.
So in simplified terms, you could say that each hair consists - similar to a steel cable
- of 390 billion strands of atoms. If you’d put them one behind the other, the strands
of a 13cm 5inch hair would already be enough to cover the distance from Earth to Mars.
But we obviously can’t stop here. An average human weights about 75 kg – 165
lbs. If we subtract 5 kilos of microbes and food or whatever’s left of it we end up
with 70 kg or 155 lbs. of meat, fat, blood, and bones.
Since life on earth is carbon-based and 65% of our body is made up of water, it shouldn’t
come as a surprise that hydrogen oxygen and carbon are the three most common elements
in our body: In fact, they make up 99% of all the atoms we are made of, so let’s just
leave out the other 1% Just under 2/3 of that is hydrogen, ¼ oxygen
and 1/10th carbon. Using the atomic mass of these elements we
can estimate that 70kg of human consist of roughly 7 octillion atoms. That’s a 7 with
27 zeros. How large is that number? Let’s put it that
way. if wed cover the entire planet, land and water combined with a mat of made of human
hairs sticking up from the ground. We would still need to duplicate the planet 140.000
times to get to 7 octillion hairs. That many atoms are in your body.
Would you line them up in a row, the resulting string of atoms would be 300 trillion kilometres
long. That’s roughly 10 parsecs or 32 light years. That would make a single human long
enough to stretch from earth to the sun and back 1.000.000 times or from the sun the nearest
star Proxima-Centauri and back 4 times. This is only possible because the atoms that
we and all the other ordinary matter in our universe are made of are so incredibly small.
And hopefully after these 10 minutes of theoretical shenanigans you now have a little better understanding
of how small exactly.