The Eleven-Mile Atomic Web Page

By Sean Carroll | June 22, 2006 12:51 pm

A web page presenting a scale-model hydrogen atom (via Cynical-C):

And you thought there was a lot of empty space in the solar system. Well, there’s even more nothing inside an atom. A hydrogen atom is only about a ten millionth of a millimeter in diameter, but the proton in the middle is a hundred thousand times smaller, and the electron whizzing around the outside is a thousand times smaller than THAT. The rest of the atom is empty. I tried to picture it, and I couldn’t. So I put together this page – and I still can’t picture it.

The page is scaled so that the smallest thing on it, the electron, is one pixel. That makes the proton, this big ball right next to us, a thousand pixels across, and the distance between them is… yep, fifty million pixels (not a hundred million, because we’re only showing the radius of the atom. ie: from the middle to the edge). If your monitor displays 72 pixels to the inch, then that works out to eleven miles – making this possibly the biggest page you’ve ever seen.

Okay, we all know that, science-wise, this is utterly bogus. Mostly because the proton and electron are not little spheres of fixed size, as our classical intuitions inevitably imagine them to be — they should be represented by wavefunctions, and the electron’s wavefunction in particular should be spread throughout all eleven miles. Admittedly, an eleven-mile web page that accurately represented the ground-state wavefunction of the hydrogen atom would have been harder to construct (although, hmm, maybe not impossible). And I’m not sure where the “sizes” of the particles came from. The proton really does have a size, about 1.5 x 10-15 m, since it’s a bound state of quarks. But the electron is a point particle, as far as we know. There are various distance scales you can associate to it, but the smallest of these is the classical electron radius, which is about twice the size of the proton diameter. John Baez explains. I don’t know how to get an electron to be one thousandth the size of a proton, unless you’re using masses rather than lengths, which is a big mistake because (in the wacky world of quantum mechanics) lengths get smaller when masses get bigger.

Still, it gives you some feeling for the instubstantiality of matter, as Geiger and Marsden long ago demonstrated. And it’s pretty cool.

  • quasar9

    Sean, it does make you think. Dimensions, density, mass and gravity.
    Anyway previous comment I made gone AWOL. Thought it would go with this post on hydrogen atom. Shall I resubmit? or just redirect to link: -Q.

  • Sean

    quasar, you should really not repost your blog entries here at all; that’s what trackbacks are for. We’ll readily delete comments that distract from the main conversation.

  • quasar9

    Hi Sean, thanks. Just thought I’d double check it wasn’t actually an electronic glitch. Anyway great post. It is a relative perspective on dimension “more nothing inside a hydrogen atom”. Anyway for those with time to read more, the comment is on the blog. Address on previous comment. Enjoy! – Q

  • Alejandro Rivero

    In this context it is interesting to remark that Copernicus argued for the vacuum space in the planetary model of the solar system by comparing it to the vacuum space in the atomic model of matter.

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  • Science


    Electrons are supposed to be Planck sized strings, according to certain people? Also, that Planck thought he had got the smallest fundamental unit of length (plus time, etc) by dimensional analysis?

    Later it was discovered that a much smaller size exists, the black hole radius/even horizon radius. Naturally the ignorant still use the Planck size. (It is convenient for them, as there is no implied physical mechanism for the Planck size which there is for the black hole size, such as trapped electromagnetic energy. I think the stringy people are deliberately steering as far away from simplicity/causality as possible. Hence extra dimensional hype.)

  • Troublemaker

    Copernicus used an analogy to a theory that didn’t exist until centuries after his death? How cool! [rolls eyes]

  • Pyracantha

    They are using a photo of the planet Neptune as the “proton” sphere.

  • Joe

    The concept that matter is made up out of ‘atoms’ is almost 2500 years old. Basically the greeks thought up the idea of atoms, and even guessed that there was a huge vacuum inside them. On the other hand, what they thought atoms were bares very little resemblence to reality.

    There is a fuller description of this here, or just google it.

  • Science

    Joe, read points #2 and #3 on the link you have given: the Greeks did not predict a vacuum inside atoms. They falsely predicted atoms are unsplittable (this prediction is so strong that the very word atom means

    “It then follows that there can be no void inside an atom itself. Otherwise an atom would be subject to changes from outside and could disintegrate. Then, it would not be an atom.

    “We know this is incorrect. In 1911, Ernest Rutherford discovered the nucleus, demonstrating in the process that a single atom is mostly empty space.”

    The first person to publish the prediction that INSIDE atoms (not beetween different atoms!) there is a void was George Louis LeSage (click my name for details) in his essay ‘Newtonian Lucretius’, New Memoirs of the Royal Academy, 1782 (Berlin: Decker, 1784), pp. 404-32.

    He had a hard time from his peers, the paper begins with the quotation:

    ‘In any matter, the first systems make people excessively conclusive, closed, cautions of others. And does it not seem that this truth is the price of some hardening of reason?’ — Fontenelle, in the eulogy of Cassini.

  • Joe


    I thought I made it clear that what the Greeks believed does not correspond to how we now know atoms to behave. I am not saying that anything about their theory was completely correct.

    I was merely pointing out to Troublemaker that the concept of atoms existed at the time of Copernicus, and that most of matter was predicted to be empty space.

    Ok, I shouldn’t have said “vacuum inside them”, my bad! I was refering to the Greeks prediction that atoms occupied a small fraction of space within matter.

    My point was only that the necessary ideas already existed for Copernicus to be able to make the analogy.

  • Science

    I was refering to the Greeks prediction that atoms occupied a small fraction of space within matter. … My point was only that the necessary ideas already existed for Copernicus to be able to make the analogy.

    But I’ve just explained the atomic idea came about in 1784, not in Greek times. If you have two atoms a distance apart, Greeks said there is vacuum between them. This has nothing to do with void inside atoms.

    Copernicus actually built on the work of Aristarchus of Samos, who had a solar system model. Aristarchus was suppressed because everyone else ignored him. Copernicus was taken more seriously because he fiddled a system with circular (not elliptical) orbits and twice as many epicycles as Ptolemy’s earth-centred universe system, to fit the data. The correct model emerged emerged a century after Copernicus when Kepler discovered elliptical orbits were correct.

  • Troublemaker

    Science has largely made my point for me, but let me clarify: the original statement was that the enormity of the empty space inside the atom somehow inspired Copernicus, and this is blatantly false. That’s all I was trying to say. Yes, the idea that matter is made up of tiny little units is very old, but the idea that these units are mostly vacuous space is not.

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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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