# What note is an oxygen molecule?January 28, 2010 10:13 PM   Subscribe

How far apart are the edges of an oxgyen molecule? How long does it take for a photon to travel that far? Expressing that photon travel time as cycles-per-second, what's pitch is it, and how many octaves away from middle C is it?
posted by Moistener to Science & Nature (20 answers total) 3 users marked this as a favorite

"What pitch is it?" kthx
posted by Moistener at 10:14 PM on January 28, 2010

How far apart? about an angstrom.

compare to middle C? uhhh.... photon = light. middle c = sound. you're trying to compare apples and oranges.
posted by chicago2penn at 10:19 PM on January 28, 2010

c / 1 angstrom is about 3*10^18 Hz (3 exahertz), or around 53 octaves above middle C.
posted by mbrubeck at 10:33 PM on January 28, 2010

The Van der Waals radius of an oxygen molecule is 2.06 angstroms, more or less. A photon would travel that distance in 6.87142036 * 10^-19 seconds. That's 1.45530319 * 10^18Hz. You'd need way more significant digits than that to tell what pitch it is, but it's about 60 octaves above middle C, more or less.

I assume that's the kind of calculation you want. Sorry it's not possible to be more precise.
posted by jedicus at 10:34 PM on January 28, 2010

Molecules don't really have "edges"; their electron clouds technically extend to infinity with an infinitesimal but non-zero amplitude. However, the two oxygen atoms in an O2 molecule are about 121 picometres, or 1.21 angstroms, apart. That corresponds to a light travel time of 4.03x10-19 seconds, or 403 zeptoseconds.

An oscillation with that period, if one existed, would therefore have a frequency of 2.47x1018 Hertz, which is pretty close to 53 octaves above the acoustic frequency of a middle C note.
posted by teraflop at 10:34 PM on January 28, 2010

tip to mbrubeck: You can do log2 in Google with lg()
posted by jedicus at 10:35 PM on January 28, 2010 [1 favorite]

Okay, fine.

An oxygen molecule is about 292 picometers.

So the answer is 51.8 octaves.
posted by aubilenon at 10:38 PM on January 28, 2010

posted by mbrubeck at 10:38 PM on January 28, 2010 [1 favorite]

oh man I wish I knew about lg() 90 seconds ago!
posted by aubilenon at 10:39 PM on January 28, 2010

An angstrom is 0.1 nanometers.

Visible light has a wavelength of between 400 and 700 nanometers. So you can't actually image an individual photon.

Middle C, according to Wikipedia, is around 261.626Hz. Converting from frequency to wavelength, we get 1/261, or 0.0038222500821784 meters, or 3,822,250.08 nanometers.

OK. So, divide by two to keep the note same while losing octaves...we see that f/2**21 is about 1.82259 nanometers, while f/2**22 is about 0.91129 nanometers. So, arguably, if the oxygen molecule was precisely one angstrom across, it'd be about a note up, or a D.

However, molecules are more like clouds than anything else, and the tolerances for individual notes are just ridiculous at that point anyway. So I'm not sure it's fair to say that Oxygen has a note.
posted by effugas at 10:39 PM on January 28, 2010 [1 favorite]

Oh I just saw the subject.

So it's between an A and an A#.
posted by aubilenon at 10:45 PM on January 28, 2010 [1 favorite]

These answers are synaptically delcious. Thank you.
posted by Moistener at 10:49 PM on January 28, 2010

Oh oh this time I have a great answer. It's about ten-and-a-half octaves higher than blue!
posted by aubilenon at 10:50 PM on January 28, 2010 [9 favorites]

How far apart are the edges of an oxgyen molecule?

Nobody can tell for sure. Oxygen molecules don't have edges.

How long does it take for a photon to travel that far?

Expressing that photon travel time as cycles-per-second, what's pitch is it, and how many octaves away from middle C is it?

There's enough inherent uncertainty in all the numbers involved that if you were to make a decent model of the oscillation you're thinking about and scale it down into the audible range by successive factors of 2, I'd expect you to hear not a pitched note but something more like a hiss, roar or rumble depending on the scaling factor.
posted by flabdablet at 11:14 PM on January 28, 2010

Molecules don't really have "edges"; their electron clouds technically extend to infinity
On the other hand, if you trapped a photon in a well that was the same shape as the well the oxygen molecule's electrons are in, even though that well extends off to infinity I think it would still have defined modes of oscillation. Much as air blown through a conical horn has frequency and timbre (harmonic structure). It should be basically the same calculation as you do in undergrad physics where you calculate the energy levels of an atom, starting with the simple electron-in-a-box model and then extending that to the actual potential well, which does extend off to infinity.

Or at least I think it's totally analogous. It's a decade or more too late for me to actually do the math, I think.

All that said, though, I like auibilenon's answer the best.
posted by hattifattener at 2:36 AM on January 29, 2010

If the real question, as suggested by the post title, is "what note is an oxygen molecule," I would suggest that rather than asking about the frequency of light whose wavelength is equal to the "length" of an oxygen molecule, you could ask what the frequency of the vibration of an oxygen molecule is, since the atoms in the molecule do vibrate and have a characteristic frequency at which they do so (several frequencies, perhaps, just as a single pipe of fixed length can play different notes). Here the ground state vibrational frequency is found to be 1580 cm-1, or 4.74*1013Hz, which would just a little below an F 37 octaves above the F above middle C. Higher vibrational modes (analagous to overtones) are the odd multiples of the ground state frequency.
posted by DevilsAdvocate at 4:48 AM on January 29, 2010 [1 favorite]

An oxygen molecule doesn't exactly vibrate because there is not middle for the ends to vibrate relative to. (This is why CO2 and methane are greenhouse gasses and oxygen and nitrogen aren't, BTW). If you move the ends, you rotate the molecule.

My summer job one year was developing pChem labs with (holds little finger to lip) a giant laser (an 8 watt argon ion job). Somewhere there is a monochromator scan of rarefied ion spinning away like mad that I did during this exercise, which the professor I was working for was still using as her example 10 years later. She said I got more peaks that anyone has since, which makes be wonder who broke what, but I digress.

What I wanted to point out was that it was peaks. Atoms live in a digital universe, which breaks the sound/light analogy pretty badly. Imagine you're tuning a stringed instrument. You pluck a string and get A flat. You tighten it and try again and get A flat. Again and again A flat. Then suddenly you get D. That's how atoms work. The are no notes in between.

Translational, vibrational and rotational energies are what you are interested in here, along with a basic workup of the Schrodinger Wave Equation (which I want to get as a tribal tattoo).
posted by Kid Charlemagne at 5:55 AM on January 29, 2010 [1 favorite]

An oxygen molecule doesn't exactly vibrate because there is not middle for the ends to vibrate relative to.

Of course it does. The two atoms vibrate relative to each other. There doesn't have to be a central atom. Google "vibrational mode diatomic molecule" if you don't believe me.

What I wanted to point out was that it was peaks. Atoms live in a digital universe, which breaks the sound/light analogy pretty badly.

I agree with the "digital universe," but I don't think it breaks the analogy. It's just that they're more akin to a bugle, with no valves or slides or anything. Bugles can't play every note, but they can still play several different notes. More importantly, just because a bugle can't play an A# doesn't mean it's broken the very concept of the musical scale or that we can't identify the notes it can play.
posted by DevilsAdvocate at 7:11 AM on January 29, 2010 [3 favorites]

DevilsAdvocate game the answer I was going to give. Molecules sing with constant vibration, humming with a sound that is way to high for us to hear, but too red to see. There's a chorus around us and in us all the time. Even apparently-empty space still rings with the echos of creation.
posted by bonehead at 11:57 AM on January 29, 2010 [1 favorite]

Philip S. Callahan reckons that insect antennae have sub-structures shaped like and functioning as tiny radio aerials tuned to the emission spectra of assorted interesting molecules including their own pheromones, and that the sensory input so obtained can account for a lot of otherwise inexplicable insect behaviour.
posted by flabdablet at 5:43 PM on January 29, 2010

« Older Why would my S.O. be so opposed to my attending...   |   What is that thing that Gordon Brown does with his... Newer »