Uploaded by numberphile on 23.10.2012

Transcript:

MARTYN POLIAKOFF: I'm a chemist.

And therefore, I suppose the most obvious number for me to

talk about is Avogadro's number.

And Avogadro's number is very big.

Surprisingly, although I'm a chemist, I can never remember

the exact value.

So let me just look it up.

It is 6.02214--

and there's some argument for further decimal places--

times 10 to the 23.

So this is a very, very big number.

And it is related to atoms and molecules.

So Avogadro was an Italian chemist who worked at the

beginning of the 19th century.

And shortly after John Dalton had proposed the idea of

atoms, Avogadro was thinking of the number of atoms and

molecules inside a flask a bit like this one.

So you imagine the gas inside here.

From those ideas, he developed the hypothesis about the

number of molecules of any gas inside a flask.

But it's easier for me to explain it to you with some

atoms here.

So imagine that we have here hydrogen; carbon, which is

black; oxygen; and uranium, which is big.

After the time of Avogadro, people started measuring the

relative mass of these atoms.

So hydrogen has a mass 1, carbon 12, oxygen 16, and

uranium 238.

These are for particular isotopes.

These weights are defined by the number of protons, the

positively charged particles, and neutrons, the neutral

ones, in the nucleus.

So for example, in carbon, you have six

protons and six neutrons.

Whereas in uranium, you have 92 protons.

And I can't work out the number of neutrons, but they

add up to 238.

I'll leave that for you to calculate.

Later chemists took Avogadro's idea and developed it into the

statement that if you take 1 gram of hydrogen, 12 grams of

carbon, 16 grams of oxygen, or 238 grams of uranium, the

number of atoms in that sample will be exactly the same.

And that number was given the name Avogadro's number in

honor of Avogadro, who started thinking about these things in

the first place.

BRADY HARAN: Professor, is that fact a lovely

coincidence?

Or is that inevitable that that would have happened

because of the way the weights of atoms work?

MARTYN POLIAKOFF: This is inevitable.

It's not a coincidence.

It's not just like the number of my birthday, December the

16th, is the same as the mass of oxygen.

It's something that's inevitably true because of the

way that these mass scale has been done.

It is the relative masses of the different atoms.

The big question is, how can you actually work out what the

number of these atoms are?

Because there's so many of them.

You can easily say that even a simple experiment that you

could do at school or college will tell you it's 6

times 10 to the 23.

But it is the decimal points and the numbers after the

decimal point that are really the key.

And the more numbers you can measure, the more precisely

you know the number.

Now, you can ask, what's the point of measuring these

things so precisely?

Why do we want to know this number so precisely?

And the reason is that it has become very important in

recent years for the definition of the unit of

mass, the kilogram.

As you know, we have a whole series of fundamental units--

the second, the meter, and so on, the ampere.

So you can define most of these units, such as the

meter, in terms of the speed of light.

But what do you use for the kilogram?

Now, there's still some argument.

But one approach is to say if we could define Avogadro's

number, then we could relate that to the mass of carbon-12

or whatever.

And then this would become a fundamental constant.

And we would no longer have to rely on a lump of platinum or

iridium stored in a vault to define what

we mean by a kilogram.

The way that people are approaching this is to measure

the mass of a lump of silicon.

The reason they've chosen silicon is

because it is an easy--

or relatively easy-- material to handle and purify.

So, they have made this spherical lump.

Imagine now this is a real ball, about the size of the

one I'm holding, but made out of silicon.

And very special silicon, the isotope silicon-28.

So that's just one isotope of silicon.

And they have grown a single crystal of silicon-28 and then

machined it into a spherical ball.

And using this ball because you can measure its diameter.

And you can measure, using X-rays, the distance between

the layers of atoms.

You can calculate the number of atoms in the ball.

You can't get the nearest atom.

But all being well, they may be able to get to 1 part in 10

to the minus 8.

That means, effectively, they can measure the number or

calculate the number to nine significant figures.

That's 6 point and then eight numbers.

And each of those digits, they can be certain, is right.

BRADY HARAN: Still a long way off the whole number.

MARTYN POLIAKOFF: It's a long way off, but it's near enough

to define the kilogram as accurately as people want.

It might be worth giving you an idea how big 6 times 10 to

the 23 really is.

And one of my friends, Colin Johnson, has calculated--

and I haven't checked his calculation--

that if you went round the entire coast of the UK and on

every sandy beach used an excavator to remove all the

sand to a depth of 1 meter.

And then you piled all that sand up somewhere and then

counted the number of grains of sand, it would be about 6

times 10 to the 23.

So if you took a lump of gold just slightly

less than 197 grams--

which, because gold's dense, is not very big, probably much

smaller than any of these balls--

in that lump there would be the same number of atoms as in

this huge pile of sand that you've got from excavating all

the beaches to a depth of 1 meter.

So you get the idea.

It's a big number.

The other thing is that most chemists don't use Avogadro's

number very often.

But what they do use is the unit that is called a mole.

And a mole is Avogadro's number of molecules.

And they talk about reactions very often in terms of moles.

Now, some of you may know that in English, and American

English, mole is the name of a small, furry creature that

burrows under the ground.

And in America, every year they celebrate chemistry on

so-called Mole Day.

And they have all sorts of cartoon moles that tries to

make people enthusiastic about chemistry.

I appear on YouTube quite frequently,

but not on this channel.

But on Brady's other channel, the chemistry channel, called

Periodic Table of Videos.

And we have a lot of fans.

And last year, on Mole Day, a fan in a school in Seattle

produced a mole.

She's called Melinda, and she's in honors chemistry 3A.

BRADY HARAN: That's the girl, not the mole.

MARTYN POLIAKOFF: Yes.

And she called this mole that she made Moltyn Moliakoff.

And I think it's rather sweet.

And some of you who have a good imagination may think

that there's a vague resemblance between

the mole and me.

I think it's great that young people, like Melinda, get so

enthusiastic about chemistry and our channel that they make

models like this.

And I would encourage you, even if you're a maths buff,

have a look at our chemistry channel.

Because chemistry is more fun than you think.

And it has bigger explosions than on maths.

[EXPLOSION SOUND]

[LAUGHTER]

-Look at--

-I'm just going to check that there's none left.

And therefore, I suppose the most obvious number for me to

talk about is Avogadro's number.

And Avogadro's number is very big.

Surprisingly, although I'm a chemist, I can never remember

the exact value.

So let me just look it up.

It is 6.02214--

and there's some argument for further decimal places--

times 10 to the 23.

So this is a very, very big number.

And it is related to atoms and molecules.

So Avogadro was an Italian chemist who worked at the

beginning of the 19th century.

And shortly after John Dalton had proposed the idea of

atoms, Avogadro was thinking of the number of atoms and

molecules inside a flask a bit like this one.

So you imagine the gas inside here.

From those ideas, he developed the hypothesis about the

number of molecules of any gas inside a flask.

But it's easier for me to explain it to you with some

atoms here.

So imagine that we have here hydrogen; carbon, which is

black; oxygen; and uranium, which is big.

After the time of Avogadro, people started measuring the

relative mass of these atoms.

So hydrogen has a mass 1, carbon 12, oxygen 16, and

uranium 238.

These are for particular isotopes.

These weights are defined by the number of protons, the

positively charged particles, and neutrons, the neutral

ones, in the nucleus.

So for example, in carbon, you have six

protons and six neutrons.

Whereas in uranium, you have 92 protons.

And I can't work out the number of neutrons, but they

add up to 238.

I'll leave that for you to calculate.

Later chemists took Avogadro's idea and developed it into the

statement that if you take 1 gram of hydrogen, 12 grams of

carbon, 16 grams of oxygen, or 238 grams of uranium, the

number of atoms in that sample will be exactly the same.

And that number was given the name Avogadro's number in

honor of Avogadro, who started thinking about these things in

the first place.

BRADY HARAN: Professor, is that fact a lovely

coincidence?

Or is that inevitable that that would have happened

because of the way the weights of atoms work?

MARTYN POLIAKOFF: This is inevitable.

It's not a coincidence.

It's not just like the number of my birthday, December the

16th, is the same as the mass of oxygen.

It's something that's inevitably true because of the

way that these mass scale has been done.

It is the relative masses of the different atoms.

The big question is, how can you actually work out what the

number of these atoms are?

Because there's so many of them.

You can easily say that even a simple experiment that you

could do at school or college will tell you it's 6

times 10 to the 23.

But it is the decimal points and the numbers after the

decimal point that are really the key.

And the more numbers you can measure, the more precisely

you know the number.

Now, you can ask, what's the point of measuring these

things so precisely?

Why do we want to know this number so precisely?

And the reason is that it has become very important in

recent years for the definition of the unit of

mass, the kilogram.

As you know, we have a whole series of fundamental units--

the second, the meter, and so on, the ampere.

So you can define most of these units, such as the

meter, in terms of the speed of light.

But what do you use for the kilogram?

Now, there's still some argument.

But one approach is to say if we could define Avogadro's

number, then we could relate that to the mass of carbon-12

or whatever.

And then this would become a fundamental constant.

And we would no longer have to rely on a lump of platinum or

iridium stored in a vault to define what

we mean by a kilogram.

The way that people are approaching this is to measure

the mass of a lump of silicon.

The reason they've chosen silicon is

because it is an easy--

or relatively easy-- material to handle and purify.

So, they have made this spherical lump.

Imagine now this is a real ball, about the size of the

one I'm holding, but made out of silicon.

And very special silicon, the isotope silicon-28.

So that's just one isotope of silicon.

And they have grown a single crystal of silicon-28 and then

machined it into a spherical ball.

And using this ball because you can measure its diameter.

And you can measure, using X-rays, the distance between

the layers of atoms.

You can calculate the number of atoms in the ball.

You can't get the nearest atom.

But all being well, they may be able to get to 1 part in 10

to the minus 8.

That means, effectively, they can measure the number or

calculate the number to nine significant figures.

That's 6 point and then eight numbers.

And each of those digits, they can be certain, is right.

BRADY HARAN: Still a long way off the whole number.

MARTYN POLIAKOFF: It's a long way off, but it's near enough

to define the kilogram as accurately as people want.

It might be worth giving you an idea how big 6 times 10 to

the 23 really is.

And one of my friends, Colin Johnson, has calculated--

and I haven't checked his calculation--

that if you went round the entire coast of the UK and on

every sandy beach used an excavator to remove all the

sand to a depth of 1 meter.

And then you piled all that sand up somewhere and then

counted the number of grains of sand, it would be about 6

times 10 to the 23.

So if you took a lump of gold just slightly

less than 197 grams--

which, because gold's dense, is not very big, probably much

smaller than any of these balls--

in that lump there would be the same number of atoms as in

this huge pile of sand that you've got from excavating all

the beaches to a depth of 1 meter.

So you get the idea.

It's a big number.

The other thing is that most chemists don't use Avogadro's

number very often.

But what they do use is the unit that is called a mole.

And a mole is Avogadro's number of molecules.

And they talk about reactions very often in terms of moles.

Now, some of you may know that in English, and American

English, mole is the name of a small, furry creature that

burrows under the ground.

And in America, every year they celebrate chemistry on

so-called Mole Day.

And they have all sorts of cartoon moles that tries to

make people enthusiastic about chemistry.

I appear on YouTube quite frequently,

but not on this channel.

But on Brady's other channel, the chemistry channel, called

Periodic Table of Videos.

And we have a lot of fans.

And last year, on Mole Day, a fan in a school in Seattle

produced a mole.

She's called Melinda, and she's in honors chemistry 3A.

BRADY HARAN: That's the girl, not the mole.

MARTYN POLIAKOFF: Yes.

And she called this mole that she made Moltyn Moliakoff.

And I think it's rather sweet.

And some of you who have a good imagination may think

that there's a vague resemblance between

the mole and me.

I think it's great that young people, like Melinda, get so

enthusiastic about chemistry and our channel that they make

models like this.

And I would encourage you, even if you're a maths buff,

have a look at our chemistry channel.

Because chemistry is more fun than you think.

And it has bigger explosions than on maths.

[EXPLOSION SOUND]

[LAUGHTER]

-Look at--

-I'm just going to check that there's none left.