Road rules0 min ago
Atoms
great question on the radio the other day tha i didnt get to hear the answer to... atoms can't be seen by the naked eye but everything is made of atoms. how many atoms would you have to combine before you could "see" them?
Answers
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A circle should be fine, as long as you are looking at it from above and it's well-lit/ coloured in contrast to the background. Humans can, after all, see 2D-shapes drawn on paper with no difficulty (OK, they're obviously really thin cylinders, but at any rate the thickness is negligible compared to its other dimensions). I think dust particles are not...
10:14 Fri 05th Dec 2014
What's the smallest visible thing, I suppose.
Answer depends a bit on how far away it is, but roughly the smallest visible objects are about 0.1mm long if they're a foot away. Also, roughly, atoms are about 0.0000003mm across at most (size of Caesium atom, apparently. So that means that you'd need about 300,000 atoms arranged in a line before you could just see them.
Answer depends a bit on how far away it is, but roughly the smallest visible objects are about 0.1mm long if they're a foot away. Also, roughly, atoms are about 0.0000003mm across at most (size of Caesium atom, apparently. So that means that you'd need about 300,000 atoms arranged in a line before you could just see them.
Smallest visible object is partially a function of the visual wavelengths of the Electromagnetic spectrum.
As far back as school biology class, I recall this being about 0.2 nanometres - but that was in the context of microscopy and I cannot think of anything familiar and be sure it fits that size range.
Things which have made me consider this very question:-
Spider silk
Cat hair (the kind which floats around and gets in your eyes)
Smoke particles
As far back as school biology class, I recall this being about 0.2 nanometres - but that was in the context of microscopy and I cannot think of anything familiar and be sure it fits that size range.
Things which have made me consider this very question:-
Spider silk
Cat hair (the kind which floats around and gets in your eyes)
Smoke particles
A circle should be fine, as long as you are looking at it from above and it's well-lit/ coloured in contrast to the background. Humans can, after all, see 2D-shapes drawn on paper with no difficulty (OK, they're obviously really thin cylinders, but at any rate the thickness is negligible compared to its other dimensions).
I think dust particles are not themselves visible, but do have a tendency to reflect a lit of light in a darkened room, making it the light you are seeing as much as anything else (I'm not so sure about smoke, but a similar explanation is likely). That could in principle make the question somewhat ambiguous, because eg it's possible to see the tracks of single electrons left in cloud chambers, but again you aren't really seeing the electron so much as the stuff it's zapped on its journey through the cloud. (Ditto Cerenkov radiation in nuclear reactors).
As far as I'm concerned the question ought to be treated as one based on taking the typical angular resolution of the human eye, converting that into the size of an object (in one or two dimensions) at a reasonably close distance (a foot is about right, because for normally-sighted people that's about the minimum focal length), and packing it with large atoms. The resulting number is bound to be out by as much as a factor of 100, but it will be good enough to give an idea.
If it's a line, the answer comes out as somewhere between 100,000 and 1 million, and if it's a circle you should square that number (and, at this level, you shouldn't care about anything more than the length of the number, so you may as well pretend that circles and squares are the same shape).
It's possible that with particularly clever lighting effects, in a sufficiently uncluttered room, you could push the answer down even smaller, but I would say that in the case of smoke particles (which are about 100 times smaller than 0.1mm), you could see them only if there's a lot gathered together, so I'm not sure that counts.
In the end, it's the technique of arriving at an answer that's the most important: throw away all the crap about the actual value of numbers, and just care about how long they are, and then a few reasonable estimates give you a ballpark figure with very little effort. Despite the numerous sources of error that might exist, it's reasonable to expect that they'd cancel each other out to a great extent: for example, in my calculation I've taking pi=4, pushing the required number up (by about 33%). On the other hand, I've also assumed that the atoms are touching each other perfectly, which is likely not to happen in reality. That would push the required number down. You could expect those two errors to cancel each other out, at least partly, making the original guess still pretty reasonable.
I think dust particles are not themselves visible, but do have a tendency to reflect a lit of light in a darkened room, making it the light you are seeing as much as anything else (I'm not so sure about smoke, but a similar explanation is likely). That could in principle make the question somewhat ambiguous, because eg it's possible to see the tracks of single electrons left in cloud chambers, but again you aren't really seeing the electron so much as the stuff it's zapped on its journey through the cloud. (Ditto Cerenkov radiation in nuclear reactors).
As far as I'm concerned the question ought to be treated as one based on taking the typical angular resolution of the human eye, converting that into the size of an object (in one or two dimensions) at a reasonably close distance (a foot is about right, because for normally-sighted people that's about the minimum focal length), and packing it with large atoms. The resulting number is bound to be out by as much as a factor of 100, but it will be good enough to give an idea.
If it's a line, the answer comes out as somewhere between 100,000 and 1 million, and if it's a circle you should square that number (and, at this level, you shouldn't care about anything more than the length of the number, so you may as well pretend that circles and squares are the same shape).
It's possible that with particularly clever lighting effects, in a sufficiently uncluttered room, you could push the answer down even smaller, but I would say that in the case of smoke particles (which are about 100 times smaller than 0.1mm), you could see them only if there's a lot gathered together, so I'm not sure that counts.
In the end, it's the technique of arriving at an answer that's the most important: throw away all the crap about the actual value of numbers, and just care about how long they are, and then a few reasonable estimates give you a ballpark figure with very little effort. Despite the numerous sources of error that might exist, it's reasonable to expect that they'd cancel each other out to a great extent: for example, in my calculation I've taking pi=4, pushing the required number up (by about 33%). On the other hand, I've also assumed that the atoms are touching each other perfectly, which is likely not to happen in reality. That would push the required number down. You could expect those two errors to cancel each other out, at least partly, making the original guess still pretty reasonable.
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