In desperation (see previous posts), I go directly to the article Periodic Table of the Elements. No answer there, either, but there is a link to "Atomic Radius." There, I am interested to learn that atoms "do behave as if they were spheres with a radius of 30–300 pm" (though their actual shape and size is less definite), with pm being picometers, that is, one one millionth of a millionth of a meter.
Here, of course, is the test of my earlier calculation. I was off by a factor of one million ... well, actually, by 10,000 to 100,000 times ... my estimate was about that much too large - which, actually, isn't too bad!
Wednesday, October 17, 2007
Avogardo
Although the article is not quite explicit about it, it seems that the final clue was detected by the Italian, Avogardo, (see Atomic Theory article) in the form of his observation that the volume of a gas is independent of its mass, and is, instead, a function of the number of molecules it contains.
But, is this the final clue? Now I'm not so sure. It did provide conclussive evidence regarding the relative mass of different atoms. How do we know, though, how many atoms are in a given amount of an element?
But, is this the final clue? Now I'm not so sure. It did provide conclussive evidence regarding the relative mass of different atoms. How do we know, though, how many atoms are in a given amount of an element?
atomic theory
In time, the article on chemistry links to Atomic Theory, and there we start to get answers to our question, in the ideal form: the history of our knowledge of the subject.
As I suspected, a real sense of atomic mass began to emerge from Lavoisier's experiments. Let's see, in the show on PBS, he ran water, or steam, through a heated iron gun barrel, and collected a gas on the other end. Since the iron combined with the oxygen in the steam, the gas that emerged was hydrogen. He then weighed the gun barrel, and found its weight to have increased. He weighed the hydrogen, and found that its weight, combined with the weight added to the barrel, equalled the weight of the water that had passed through the barrel.
Where it went from there, exactly, I'm not sure, but Lavoisier and those who proceeded from his work could tell that substances were being divided and recombined in certain proportions, which gave them evidence about the composition of the substances.
I must read further. Absolutely do link to these articles, as they are enthralling. (Note: they could use a bit of proof-reading.)
As I suspected, a real sense of atomic mass began to emerge from Lavoisier's experiments. Let's see, in the show on PBS, he ran water, or steam, through a heated iron gun barrel, and collected a gas on the other end. Since the iron combined with the oxygen in the steam, the gas that emerged was hydrogen. He then weighed the gun barrel, and found its weight to have increased. He weighed the hydrogen, and found that its weight, combined with the weight added to the barrel, equalled the weight of the water that had passed through the barrel.
Where it went from there, exactly, I'm not sure, but Lavoisier and those who proceeded from his work could tell that substances were being divided and recombined in certain proportions, which gave them evidence about the composition of the substances.
I must read further. Absolutely do link to these articles, as they are enthralling. (Note: they could use a bit of proof-reading.)
a clue: gas laws
If I go to the history of chemistry, via Wikipedia, I learn - among many very, very interesting things - that, starting in about the 1660s (in Europe), gas pressure was carefully observed, and then in the early 1700s it was explained as the kinetic energy of gas molecules.
Read the details at Wikipedia under Boyle's Law.
The kinetic theory must mean that gas pressure is caused by the cumulative impact of numerous molecules colliding with a vessel wall, or the surface of an object. If we know the total mass of the gas in a vessel, for instance, we may be able to calculate a ratio of the number of collisions that mass would need to make and the velocity of each collision, to produce the observed pressure.
This doesn't tell us how many atoms are in a given amount of gas ... it just hints at the number, or at the idea that there are many atoms in a volume of gas.
Read the details at Wikipedia under Boyle's Law.
The kinetic theory must mean that gas pressure is caused by the cumulative impact of numerous molecules colliding with a vessel wall, or the surface of an object. If we know the total mass of the gas in a vessel, for instance, we may be able to calculate a ratio of the number of collisions that mass would need to make and the velocity of each collision, to produce the observed pressure.
This doesn't tell us how many atoms are in a given amount of gas ... it just hints at the number, or at the idea that there are many atoms in a volume of gas.
first yahoo physics listing
No link directly to something on the history of physics, which is what I'm looking for now. (See next post for link to site.)
Now, its clear, I think, that Mendelev had a definite sense of atomic weights, and that means he knew, much more definitely than I do now (as represented by my calculations in the previous post) how many atoms are in a given mass. How did he know that?
Incidentally, I just read that the Planck Length is one billion-trillion-trillionth of a centimeter. How does that compare with my calculation? Let's say our stone is a cube, 100 centimeters to a side. Let's say each pebble is one centimeter across. One face of the cube, then, is occupied by 100x100=10,000 pebbles. A pebble, then is 100 grains of sand across, and a grain of sand is 100 particles of powder across, and a particle of powder is 100 atoms across, so the size of an atom (its width) is 100(grains)x100(particles)x100(atoms)=10,000x100=100,000 times smaller than a pebble, which is 1/100,000th of a centimeter ... much, much larger than the Planck Length. (Of course, I have not the slightest idea how accurate my estimate is.)
Now, its clear, I think, that Mendelev had a definite sense of atomic weights, and that means he knew, much more definitely than I do now (as represented by my calculations in the previous post) how many atoms are in a given mass. How did he know that?
Incidentally, I just read that the Planck Length is one billion-trillion-trillionth of a centimeter. How does that compare with my calculation? Let's say our stone is a cube, 100 centimeters to a side. Let's say each pebble is one centimeter across. One face of the cube, then, is occupied by 100x100=10,000 pebbles. A pebble, then is 100 grains of sand across, and a grain of sand is 100 particles of powder across, and a particle of powder is 100 atoms across, so the size of an atom (its width) is 100(grains)x100(particles)x100(atoms)=10,000x100=100,000 times smaller than a pebble, which is 1/100,000th of a centimeter ... much, much larger than the Planck Length. (Of course, I have not the slightest idea how accurate my estimate is.)
Tuesday, October 16, 2007
a problem with the previous analysis
A problem is: a stone is composed of various size pebbles, some of which are similar to grains of sand. Some of them might be grains of sand.
One way to resolve this: a particle of powder might be composed of collections of atoms, resembling pebbles, in a matrix of atoms, equivalent to a sandy cement holding the pebbles together in a stone.
The alternative (not necessarily exclusive) is large atoms in a matrix of smaller atoms.
One way to resolve this: a particle of powder might be composed of collections of atoms, resembling pebbles, in a matrix of atoms, equivalent to a sandy cement holding the pebbles together in a stone.
The alternative (not necessarily exclusive) is large atoms in a matrix of smaller atoms.
Size of Atoms
Did the philosopher make statements about the likely size of atoms?
A rock might be the size of one's hand. It might subdivide into, say, one million pebbles. Let's say each of those subdivides into one million grains of sand. Let's say each of those subdivides into one million particles of powder. Each of those subdivides into one million atoms.
1,000,000(pebbles)X1,000,000=1,000,000,000,000(1 trillion grains of sand) ...X1,000,000=1,000,000,000,000,000,000(1 million trillion particle of powder)
...X1,000,000=1,000,000,000,000,000,000,000,000(1 trillion trillion atoms)
This sounds like it could be right (in a general way).
A rock might be the size of one's hand. It might subdivide into, say, one million pebbles. Let's say each of those subdivides into one million grains of sand. Let's say each of those subdivides into one million particles of powder. Each of those subdivides into one million atoms.
1,000,000(pebbles)X1,000,000=1,000,000,000,000(1 trillion grains of sand) ...X1,000,000=1,000,000,000,000,000,000(1 million trillion particle of powder)
...X1,000,000=1,000,000,000,000,000,000,000,000(1 trillion trillion atoms)
This sounds like it could be right (in a general way).
Elements
According to Timothy Leary, Mendelev devised the Periodic Table of Chemical Elements in 1868. (The Game of Life, pages 11-15.)
I hypothesize that Mendel had some idea about, say, the size of atoms, when he undertook his analysis. What was science saying about that at the time, and who was saying it?
From school days, I remember that one of the Greeks hypothesized the existence of atoms. As the story went, he suggested the existence of some part of things that cannot be further divided. Is that really what he asserted? It seems a bit counterintuitive.
But, how might the philosopher have arrived at his conclusion? Here's my reasoning: Consider something like a crumbly stone. It is a single object, that is clearly composed of numerous smaller objects. The texture of one of those smaller objects is similar to the texture of the stone ... in fact, we might be able to see some of those smaller objects crumbling into still smaller objects - grains. And those smaller objects, in turn, have, again, a texture that is similar to the texture of the whole stone, in terms, say, of hardness ... and also in terms of granularity. We might be able to see - visual inspection - hints of granular patterns in a grain of sand ... and a grain of sand might even be crumbling into still smaller particles - powder.
Beyond this, simple visual detection provides limited or little information. We are left to surmise that a grain of powder subdivides in turn into something we cannot readily detect. Is that an atom?
Returning to the question of what the philosopher meant by his idea of the atom, it seems more logical, to me, to think it was such a next step in size. Or, did he have extra information. It does appear (based on more modern information) that atoms indeed are quite hard to divide. Are they harder to divide than, say, rocks? Some rocks are quite tenacious.
I hypothesize that Mendel had some idea about, say, the size of atoms, when he undertook his analysis. What was science saying about that at the time, and who was saying it?
From school days, I remember that one of the Greeks hypothesized the existence of atoms. As the story went, he suggested the existence of some part of things that cannot be further divided. Is that really what he asserted? It seems a bit counterintuitive.
But, how might the philosopher have arrived at his conclusion? Here's my reasoning: Consider something like a crumbly stone. It is a single object, that is clearly composed of numerous smaller objects. The texture of one of those smaller objects is similar to the texture of the stone ... in fact, we might be able to see some of those smaller objects crumbling into still smaller objects - grains. And those smaller objects, in turn, have, again, a texture that is similar to the texture of the whole stone, in terms, say, of hardness ... and also in terms of granularity. We might be able to see - visual inspection - hints of granular patterns in a grain of sand ... and a grain of sand might even be crumbling into still smaller particles - powder.
Beyond this, simple visual detection provides limited or little information. We are left to surmise that a grain of powder subdivides in turn into something we cannot readily detect. Is that an atom?
Returning to the question of what the philosopher meant by his idea of the atom, it seems more logical, to me, to think it was such a next step in size. Or, did he have extra information. It does appear (based on more modern information) that atoms indeed are quite hard to divide. Are they harder to divide than, say, rocks? Some rocks are quite tenacious.
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