Pique the Geek 20091129. The Size of the Nucleus

( – promoted by buhdydharma )

Atomic theory had been pretty well established well before the turn of the previous century, but no one knew much about the nature of atoms other than that the atoms of different elements had different masses (later advances revealed that they have different numbers of protons), and were composed of a positive nucleus and negative electrons, with positive and negative charges being equal in number so that the net electrical charge was zero.

Electrons were definitely established by J. J. Thomson in 1897, and he postulated that atoms were more of less continuous lumps of matter matter with positive charge in which lumps of negative charge (electrons) were embedded, although they had some freedom of movement.

With this model, the atom should be have a more of less continuous distribution of mass.  It was known at the time that electrons were much less massive than the positive bits (the proton had not been identified as the unit of positive charge), so that basically the atom resembled a plum pudding.  Americans would more easily identify with something more like a raisin muffin, since we are not big on plum pudding, but the idea is the same.

Ernest Rutherford was what we would now call the principal investigator in the effort to determine if this were so.  The actual people who conducted the experiments were

Ernest Marsdon, an Englishman, and Hans Geiger, a German (yes, the Geiger behind the Geiger counter).  The idea behind the experiment was pretty simple:  shoot subatomic particles at something and see where they went.

If the plum pudding model were correct, the particles should have a fairly small deflection that would, through geometric considerations, should tell something about the density and charge distribution within the atom.  The hard bits were to decide what to shoot and what the target should be.

They chose alpha particles, which are high energy helium nuclei that are part of many radioactive decay processes.  Radium bromide was chosen as the source of these particles, since it was easy to handle (the health effects of the intense radiation were not known at the time) and provided a strong source of the alpha particles.  The material was placed in a thick lead canister into which a small hole was drilled to provide a narrow beam of alpha particles.

The target that they chose was a thin gold foil.  There were a couple of reasons for that.  First, gold can be beaten into sheets thinner than any other metal.  Whilst these sheets are physically fragile, they are quite inert chemically, so the air would not cause them to corrode, so once they had one mounted successfully in the holder, it would be stable if not touched.  The thinness is important, because alpha particles are completely stopped by a sheet of regular paper.  (The reason that alpha emitters are so dangerous from a radiological standpoint is that when ingested, the radionuclides that emit them are taken up into the bone, for the most part, and alpha particles irradiate the blood forming tissues, causing all sorts of problems.  Marie Curie died from this, by the way).

So they sat up their alpha source and pointed the pencil of particles at their gold foil.  Now, you can not see alpha particles, but you can see the light that they produce when they strike a screen of zinc sulfide, the same material in black and white TeeVee screens.  So they got in a darkened room and looked at the size of the spot on the screen before and after putting the gold foil in between. They expected the spot to enlarge somewhat, if the plum pudding model were correct.  In reality, the spot did not enlarge at all, but it did diminish in intensity, but not enough for the eye to see.

The scientists sat around for a while as said, “Where are those particles going?  They HAVE to hit something!”  They changed their screen from flat, where the foil was between the source and the screen, to circular such that the screen went all the way around the whole apparatus, so that there was screen 360 degrees around the foil in the plane of the beam.  They turned off the lights, and opened the lead orifice to allow the alpha particles to hit the screen (without the foil), and, NOTHING.  There was just the same spot where the beam hit the screen in a straight line from the exit port.

Then they put the gold foil in the beam.  Fortunately, zinc sulfide is sensitive enough to give a flash from impact from a single alpha particle, and they began seeing flashes far from the main spot.  Some of those flashes were even 180 degrees away from the main spot, in other words now and then an alpha particle would be deflected back towards the source, rather then going right through the foil or being deflected.  Rutherford said later

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive centre, carrying a charge.

The plum pudding model of the atom was completely inconsistent with these observations.  It has been said that the experiment was not sufficient to determine whether the nucleus was positively or negatively charged, but this is not so.  The mass of the electron has already been estimated fairly accurately, so there was no way that the electron could be the nucleus since it was already known that the great bulk of the mass of the atom was NOT the electrons.  Thus, although this particular experiment did not say, that was already established information and this experiment was not inconsistent with that.

The size of gold atoms was fairly well known at the time, so Rutherford made some estimates about what was going on in this system.  First, you have to remember that until an alpha particle comes close to a nucleus, it is actually attracted to an atom, since the bulk of the space in the atom is occupied by what we know know, in quantum mechanical terms, as electron density, which is charged negatively.  Thus, the positive alpha particles are attracted and are accelerated towards an atom.  Most of the time they come no where near a nucleus, and are then are slowed down as they pass out of the negative charge an equal amount to the acceleration whilst approaching, leaving the region pretty much unchanged.

Now, some alpha particles pass near enough a positive nucleus to be deflected to a relatively small amount, and the relative number of spots with only meagre deflections could be estimated.  The number of spots that were deflected nearly 180 degrees could then be compared to the ones deflected only a little and a rough estimate of the size of the nucleus thus extrapolated.  Rutherford could not come up with a specific radius for the nucleus, but he was able to estimate an upper limit as to what it could be, and suspected that it was significantly smaller.  His upper limit is somewhat larger than the modern experimentally derived ones, but he said that it was an upper limit.  He estimated the limit to be 3.4 x 10^-14 meters.  Using the more modern equation

R = r₀A^1/3

where r₀ = 1.25 × 10^-15 m and A is the sum of the protons and neutrons in a given nucleus, (for gold, 197 since that is the only natural isotope) the radius comes to

7.27 x 10^-15 m

Now the atom was understood much better than before, but there was still much to do.  Remember, quantum mechanics had not been developed at the time.  Einstein had just left his clerking position at the Swiss Patent Office, and had only a couple of years before started to think about quantum mechanics (he later rejected quantum mechanics, largely because of the Heisenberg Uncertainty Principle, saying that …” God does not play dice with the Universe…”.  The problems remaining with atomic theory were many, and it was not until Niels Bohr came up with a mathematically consistent model that explained the line spectra of the hydrogen atom did it approach our concept of it now insofar and electronic energy levels, motion, and placement are concerned.

Most of us still have the Bohr model of the atom as our concept of it, with the nucleus like the sun in the middle and the electrons in well defined, circular orbits around it.  This is far from accurate, and we now know that no electron has a completely defined position and speed around any nucleus.  This is a direct result of the Uncertainty Principle, by the way.

Our visualization of the atom has been advanced by theory and experiment, and continuously refined for decades.  A couple of installments I wrote about the shapes of electronic orbitals, which were purely mathematical constructs.  Well, in the latest issue of Scientific American is a newsblurb about the shapes of s and p orbitals, with PICTURES taken with a field-emission microscope here.  These are not mathematical models; they are actual pictures of the electron density in real atoms.  Pretty cool, huh?

Well, you have done it again.  You have wasted another perfectly good set of photons reading this tripe, and even though Tiger Woods agrees to talk to the police when he reads me say it, I always learn much more writing this series than I could possibly hope to teach, so keep those comments, questions, corrections, and other issues coming.  Remember, no technical or scientific issue is off topic in this series.

As a followup to the recent installment on coins, I have completed the statistical analysis for recently searched United States cents.  These were bank rolls of circulated cents, obtained in Richmond, KY over the past several weeks.  Out of 10,000 coins, there were 2,797 95% copper ones, 27 of which were Wheat Ears.  That works out to right at 28% of the cents in this sample being 95% copper, and only 0.27% of them being Wheat Ears, meaning that the number of Wheat Ears in this sample were just under 1% of the population of copper coins.  33 coins were Canadian, about half being 95% copper.  Next time I am refining my statistics to include “S” mintmark cents and actual copper versus zinc Canadian ones.

Warmest regards,

Doc

Crossposted at dailykos.com