The speed of atoms

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Up: Intuitive feel

This page is meant to give an intuitive feel for the violence of the motions at the nanoscale via an interesting uncommon and maybe novel perspective that goes together well with the topic of this wiki.
If you, the reader is looking for a conventional technical introduction to thermal motion this is probably not the right place here. There are plenty of resources on the web that are much better than what could be presented here, please consult those.

Air molecules as fast as bullets

Or: How every human on earth is hit by the the equivalent of a relentless non stop barrage of handgun bullets from birth to death.

As we all know being hit by a bullet from a handgun is not good for health. But what if you split the bullet into many many small pieces and let them hit you with the same speed but now evenly distributed from all sides (assuming no breaking through air resistance)? Would you dare to try this?

What if I told you that you already did try this for your whole life?

When we assume that:

  • the bullet is split up into all its individual atoms such that there now is plenty of space between them
  • the bullet is converted into a spherical shell of dispersed atoms
    (a shell with of about a thousandfold volume and a thousandth of the density of the original bullet)
  • the shell is concentrically coming at you (matching your body shape) and hitting you with the original non-reduced speed

then you probably would not even notice being hit.


What the split up atoms of the bullet bullet would do to you is actually very similar to what the molecules of the air do to you.

If one looks at free flying atoms (or very small molecules) like the ones one finds in air, then their speed of motion lies around the speed of sound. That is the main constituents of our earth's atmosphere (dinitrogen N2 and dioxygen O2 zip around with speeds that average out at about 340m/s (at normal conditions). This is about the speed of a bullet of a hand gun.

In contrast to the bullet, air molecules do hit you permanently and relentlessly instead of just for roughly 30 microsceconds. Thirty microseconds is the time it takes for a 1cm long (hopefully atomically dispersed) bullet to hit you tip to tail. Well since this "impact" would add up atop the normal air pressure it would double it (equivalent to an easily diveable water depth of 10m) for the brief period of these 30 microseconds. But you would still likely notice barely any effect since 30 microseconds are so short that due to the inertia of mass of your skin there will barely be any effect.

How "speed" is "faster" when you are smaller as an observer

Being smaller makes motions with same speeds seem to be faster. Driving an 1:10 RC car with FPV (first person view) remote vision at about 10m/s=36km/h feels like driving with 100m/s=360km/h but in reality it is still the 10m/s=36km/h. What we actually experience as "speed" is the frequency with which we are passing some stuff in the environment.

The speed of sound air molecules fly around with is pretty fast even for macroscale observers and macroscale objects they fly past by. So how fast will this feel if you scale yourself down to the nanoscale. Or reversely (more practically archivable) scale the nanoscale up to your size.

Half the speed of light when atoms get scaled up enough to become visible to good eyes

Scaling up just size by an ideal scaling factor of 500.000 (See: Magnification theme-park) and leaving time untouched/unchanged/unscaled/as-is leads to a scale-up of speeds that accurately represents the experienced speeds. The speeds of real size air molecules then go from "only" ~340m/s at 1:1 scale up to an experienced pseudo-speed of scaled up air molecules of about 170.000.000 m/s at the new 500.000:1 scale. This is a bit more than halve the speed of light.

There is absolutely no way to intuitively ascertain that kind of speed.
Now add all the inter-atomic collisions with the very close by other atoms. (And note that in "model-air" spaces between 0.1mm scaled up model-atoms are about 1mm big (not the mean free path length but the side-length of a box in which one finds one model-atom at average) since the density of air is about 1/1000th of solids with densely packed mutually contacting atoms.)
What you get is mind bogglingly ridiculous pinball motion. Unfortunately beyond any point where it can be made intuitively graspable.

This ultra rapid sequence of changing encounters ("intermolecular mixer meeting") has pretty wild consequences. Among others provides an important part for the explanation why life could emerge just by accident. That is: Why evolution worked and works.

Keping "speed" equally "fast" when getting smaller as observer

Cinematic slow-motion by using the one special time scale factor that naturally suggests itself

To have a more natural feel for the speeds at the nanoscale, time must be scaled in the opposite direction than space. While magnifying size we need to shrink time (aka slow-motion). One wants to scale time in such a way that operation frequencies are kept natural when transferred to the model that is scaled up in size.

Using this approach still leaves us with hair diameter (0.1mm) model air molecules bouncing around at the speed of sound ~340m/s while now additionally we need to wait 500.000 seconds (almost 6 days!) in our model for one real second to pass.

So a we have a model-molecule (scaled up to hair diameter) bouncing around with the speed of sound. in a densely populated molecular environment (scaled up a heap of beard stubbles) for about six days that is thereby emulating just one real second. Just one. Let that sink.

Ok, this is not very intuitive. Now we have distributed one totally and utterly unintuitive and unimaginably big quantity (halve the speed of light) into two still quite unintuitive and unimaginably large quantities (speed of sound and a quite big stretching of time). This is not much better than before, if even, isn't it? Well yes, but ...

Bigger parts (nanomachinery) gets slow enough to allow for a more intuitive feel

Where this scaling method that also scales time not only space will become more useful for an attainment of an intuitive feel is when it comes to parts that are just a slightly bit bigger than molecules (nanomachinery crystolecules). Such parts already move quite a bit slower than single molecules. In fact usually slow enough that they can conveniently be traced around by eye. With our intuitivity preserving "magnification factor" of 500.000 typical nanomachinery operation frequencies e.g. 1MHz will get downscaled to just 2Hz.