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Saturday, November 21, 2009

Velocity, Part 2

I've been trying to understand why Alpha particles (from Americium 241 which is used in smoke detectors) is so harmless and Neutron radiation is so dangerous. Especially since Alpha particles weigh four times as much as neutrons and their initial velocity is higher. Fast Neutrons travel around 15km/s (kilometers per second) and Alpha particles travel around 20 km/s.

The essential difference seems to be that Alpha particles carry an electrical charge, and Neutrons, being neutral, do not. Still, I wonder. Neutrons can travel miles in air before they hit anything. Alpha particles only manage to get a couple of inches. It must be electrons, which are the only particles that carry a negative charge. But under normal circumstances, all the electrons are busy, so just how does this work? It's just weird.

Atoms have a tiny nucleus that is surrounded by a cloud of electrons, much like you could have a cloud of fruit flies around an orange, except the orange is the size of a mustard seed, and the cloud is as big as your house.

When an Alpha particle is kicked out of a heavier atom due to radioactive decay, it travels through the cloud surrounding this original atom and it doesn't pick up any electrons there. It just zooms right through the cloud, otherwise we wouldn't be having this discussion. This leaves the atom with a couple of extra electrons, and who knows what happens to them. I imagine they will probably wander off with some positively charged swain eventually.

But now our positively charge Alpha particle is on it's way at measurable fraction of the speed of light, about 5% actually. Light travels at about one foot per nanosecond. (Number of feet per mile (5280) times the speed of light in miles per second (186,000) is roughly equal to one billion feet per second, and there are a billion nanoseconds in one second. So one foot per nanosecond, more or less.) So our Alpha particle travels about 5/8 of an inch in one nanosecond. (Another way to think of a nanosecond is to look at your computer. A computer that operates at one gigahertz (GHz) does one operation per nanosecond. A computer that runs at 3 GHz will do three operations in one nanosecond.)

Atoms in air are widely separated, so an Alpha particle is liable to go some distance before it actually hits one. When it does impact one it will most likely just go through the cloud of electrons (big as a house). It is unlikely to hit the nucleus (small as a mustard seed). Now it is unlikely to pick up an electron from this, after all, when it was kicked out of it's parent atom it didn't manage to pick up any electrons. And even if it did pick up one, it's not going to slow it down. Compared to an Alpha particle an electron weighs next to nothing. It's like comparing a life preserver to the Titanic.

So I think what we've got going on here is electron drag. Atoms taken as a whole are neutral, they have the same number of positively charged protons as they do negatively charged electrons. At some distance from the atom, these charges cancel each other out and no charge is apparent. But the protons are all in the nucleus, and the electrons are all in the cloud, so when you get right up close to an atom, closer than the electron is to the nucleus, you are going to feel some of the negative charge from the electrons. This is what is dragging on the Alpha particle and slowing it down. It's not much force, but atoms are tiny, and even a small amount of air contains zillions of them. So as the Alpha particle travels through air, every few nanometers it comes close enough to an air molecule that it feels the attraction from the electrons, and this slows it down just a hair. You do that a few zillion times and pretty soon your charged alpha particle is at rest. It may even have captured a couple of electrons, making it neutral, but leaving a couple of air molecules ionized.

I would check my numbers, but I am pretty much worn out from trying to sort all this out. I spent several hours yesterday trying to find the information I wanted and then I finally found this statement (on this page):

Oxygen molecule flies into nitrogen gas

"How far can we expect the O2 to get before it hits an N2? The average distance before a collision is the mean free path. Let’s try to picture how much room there is to fly between these fixed N2 spheres. (Bear in mind that the picture above should be three-dimensional!) We do know that if it were liquid nitrogen, there would be very little room: liquids are just about incompressible, so the molecules must be touching. Roughly speaking, a molecule of diameter d will occupy a cubical volume of about d3 (there has to be some space left over—we can pack cubes to fill space, but not spheres.)
"We also know that liquid nitrogen weighs about 800 kg per cubic meter, whereas N2 gas at room temperature (and pressure) weighs about 1.2 kg per cubic meter, a ratio of 670. This means that on average each molecule in the gas has 670 times more room—that is, it has a space 670 times the volume d3 we gave it in the liquid. So in the gas, the average center-to-center separation of the molecules will be the cube root of 670, which is about 8.75d. So the picture is a gas of spheres of diameter d, placed at random, but separated on average by distances of order 10d. It’s clear that shooting an oxygen molecule into this it will get quite a way. Let us emphasize again that this picture is independent of the actual size of d: we’re only considering the ratio of mean free path to molecular diameter."
So I stand by my supersonic-aircraft-hooking-a-zillion-mailbags-and-the-straps-break analogy.

Update January 2017 replaced missing image.

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