Re: How can people count subatomic particles?

Greetings, Karin:

It took a great deal of trial and error before anyone could count 
subatomic particles with any degree of accuracy.  And progress of any sort 
didn't really occur until the mid-1800s or so.  After all, before one can 
count subatomic particles, it might be wise to first learn how to count 
ordinary atoms -- and then to learn how it was discovered that there ARE 
such things as subatomic particles!  For atoms, there were two approaches 
that both worked to some extent; one was followed by the chemists, and one 
was followed by the physicists, but both needed each other before the task 
was finished.  I'll present an overview of the physicists' approach first.

The study of static electricity (or electrostatics) led to the discovery 
that any electrically charged object, when compared to any other 
electrically charged object, appeared to acquire charge in discrete units. 
 This was verified by delicate experiments which measured the attractive 
or repulsive force between pairs of charged objects: the amount of force 
ALWAYS changed by an amount which could be interpreted in terms of 
multiples of discrete charges interacting with each other.  This led to 
computations of what was then considered to be a fundamental unit of 
electric charge.  The nature of the object that possessed this charge was 
unknown, however.  (A number of years passed after those computations, 
however, before anyone actually caught some loose electric charges in a 
vacuum chamber, thereby discovering the electron.)

Well, that era was also aware of the 'electrochemical cell' (often termed 
a 'battery' these days,  although a REAL battery is actually a connected 
grouping of cells).  Such cells are sources of steadily flowing electric 
currents.  Simple devices also existed which were the equivalent of the 
modern electronic-circuit 'capacitor'; they could accumulate some flowing 
electric current, and acquire a static-electric charge.  After more 
experiments, it could be determined with reasonable accuracy just how much 
current it took to produce a given static charge; this meant that it 
became possible to compute just how many electric charges were flowing 
down a wire, during the normal operation of an electrochemical cell.  One 
ampere of current is about 6.24 x 10E18, or 6,240,000,000,000,000,000 
electric charges flowing per second.  Don't let this number boggle you too 
much; electrons actually flow rather slowly through a wire (millimeters 
per second, maybe); it is just that atoms are so small that equivalently 
vast numbers of them exist in the cross-sections of even fairly small 
copper wires (and each copper atom can donate up to two electrons to the 
current flow, although that wasn't known when the above computation was 
first made).

The next piece of progress came from electrolysis experiments.  This is a 
process by which electric currents can be used to break apart various 
molecules into smaller pieces, frequently atoms.  If an appropriate pure 
substance is added to pure water, then as it dissolves, the substance's 
molecules will split apart, into smaller electrically charged pieces, yet 
stay mixed.  This is enough to make the water electrically conductive, so 
a pair of electrodes are placed some distance apart into the water.  When 
a voltage is applied, flowing current takes the form of the dissolved 
charged particles migrating, one type towards each electrode.  AT the 
electrodes, various interesting things can happen (for example, if the 
dissolved substance is sulfuric acid, then interactions of charged 
particles in the solution with the electrodes will result in the bubbling 
forth of hydrogen and oxygen gasses, one at each electrode).  It was 
discovered that certain substances such as silver could be obtained in 
extremely pure form via electrolysis.  The trick was to dissolve a silver 
compound into the water (silver nitrate, if I recall correctly), and use 
two electrodes made of impure silver, one very fat one one very skinny.  
The electric current was applied such that silver in the solution would 
tend to accumulate upon the skinny electrode.  Meanwhile, the nitrate 
portion of the dissolved compound interacted with the impure silver so as 
to carry some of it into the solution.  The net effect was for silver 
particles to acquire a charge and migrate from the fat electrode, through 
the solution, to the skinny electrode (thereby BEING the essence of the 
electric current in the solution), where they gave up their acquired 
charges.  Impurities simply dropped to the bottom of the electrolytic 
cell, and stayed there.  One ends up with a fat pure silver electrode 
(with an impure core, but if a layer was peeled off the outside and used 
as a new skinny electrode, all following electrolysis operations would 
yield fat electrodes of the same high purity throughout).

Anyway, the point of the preceding is that THIS was discovered:  A certain 
amount of current applied for a certain amount of time always resulted in 
the same WEIGHT of silver accumulation upon the skinny electrode.  This 
meant that there had to be a simple correspondence between the numbers of 
electric charges in the flowing current, and the numbers of atoms that 
accumulated.  But how many charges were associated with each silver atom? 
 That is where the chemists were needed....

During the 1800s the chemists were busy reacting carefully weighed amounts 
of many substances with each other, and noting the weights of the 
resulting compounds.  One of the products of this experimentation came to 
be known as the Law of Conservation of Mass; the total weights before and 
after any chemical reaction were always the same (to the limits of the 
measuring instruments of the era; nowadays we know that mass can be 
converted to energy and vice-versa, so nowadays we have the Law of 
Conservation of Mass/Energy).  I might mention here that chemists were 
much looser in their definitions of 'weight' and 'mass' than physicists; 
however, for chemists the distinction really is rather ignore-able, so 
they did, assuming them to be equivalent for all practical purposes.

The thing that chemists were mostly interested in was "complete" 
reactions.  It is all very well if you want to react 10 grams of Substance 
A with 20 grams of Substance B, but when the reaction is over, and you 
still find yourself in possession of 15 grams of Substance B, 15 grams of 
Substance C, and zero grams of Substance A, then you must conclude that 
the "natural" ratio of reactants in this case is 2 parts of A to 1 part of 
B, by weight at least.

And reactions were seldom that simple.  One gram of hydrogen could 
completely react with 8 grams of oxygen to make water, or with 16 grams of 
oxygen to make hydrogen peroxide; 12 grams of carbon could react with 16 
grams of oxygen to make one type of gas, or with 32 grams of oxygen to 
make a different type of gas, or with 4 grams of hydrogen to make a third 
type of gas.  Eleven grams of sodium could completely react with one gram 
of hydrogen and sixteen grams of oxygen to make sodium hydroxide (or, 
strangely, with about 35-and-a-half grams of chlorine to make table salt). 
 And so on, and so on, and so on.

To make a long story short, after reacting hundreds of different things 
with each other, and noting the proportions involved, it became possible 
to note this trend:  Each atom had a limited number of ways it could "hook 
up" with other atoms, and frequently there was only one such way.  
Hydrogen and sodium only had single hooks, magnesium and calcium had two, 
aluminum and nitrogen had three, copper sometimes had one and sometimes 
had two, chlorine usually had one, but on occasion exibited three, five, 
or seven(!), carbon usually had four, but sometimes had two, and oxygen 
always had two, even though it could occasionally generate the illusion of 
having one (the chemical formula for hydrogen peroxide is H2O2; the two 
oxygens each use one hook to link together, and their second hooks to 
connect the hydrogens).  Potassium and fluorine always had only one hook, 
silicon always had four, argon had NONE, iron sometimes had two and 
sometimes three, sulfur usually had two, tin and lead had either two or 
four, mercury usually had two, phosphorus and arsenic had either three or 
five, and so on, and so on, and so on.  It took decades to sort the mess 
out, because part of the mess was the task of determining the chemical 
formulae of hundreds of compounds.  And the list of known chemical 
elements kept growing throughout that entire century, leading to even more 
compounds to figure out!  In the end, though, the chemists had a pretty 
accurate picture of the RELATIVE WEIGHTS of all those atoms.  They didn't, 
however, have any way of knowing how many atoms of a given kind it took to 
add up a given number of grams....

What the chemists discovered, that the physicists badly needed to know, 
was that a silver atom had only one hook.  This meant that a known number 
of electric charges flowing through an electrolytic cell was associated 
one-for-one with the silver atoms accumulating in known amounts of weight 
on the skinny electrode.  The weight of a single silver atom could now be 
computed! -- and by association of ratios, thanks to the chemists' 
efforts, so could the "atomic weights" of all those other chemical 
elements.  The era of counting atoms en masse was at hand.

Almost immediatly, however, it was noticed that if flowing charges in an 
electrolytic cell contributed to the accumulation of whole atoms, then 
shouldn't those flowing charges be considered actual pieces of atoms?  It 
took a while for this seemingly obvious deduction to become accepted, 
because of the long long tradition (ever since ancient Greece!) of 
thinking of atoms as fundamental things that could not be subdivided.  Yet 
there was the sheer number of different kinds of chemical-element atoms to 
ponder:  Why so many "fundamental" objects?  And what of the similarities 
in chemical properties among various groups of elements that many had 
noticed, and eventually became organized into a Periodic Table?  Doesn't a 
periodic repetition of obvious properties hint at some controlling hidden 
properties and/or substructure?

Then it happened that physicists got to playing with electricity inside of 
sealed/evacuated glass objects, and the existence of the electron, that 
charge-carrying piece of an atom, became known.  Radioactivity was 
discovered about the same time, and a gadget known as the 'scintillometer' 
was invented.  Placed near a mildly radioactive substance such as 
pitchblende (uranium ore), in a dark room one could see individual 
scintillations of light upon the surface of the gadget.  These were caused 
by individual particles zooming away from the radioactive substance, and 
striking the special surface of the scintillometer.  How's that for direct 
eyeball count of subatomic particles?  Dangerous!  One should avoid 
radioactivity whenever possible (but this wasn't known for decades after 
its discovery).  Nowadays we have Geiger counters, which work in any kind 
of light, and count subatomic particles (and gamma-radiation photons) 
electronically.

Then the atomic nucleus was discovered, and high-voltage electrical 
equipment provided a way to count the electric charges hidden there.  Such 
equipment lets us generate a high-speed beam of electrons in a vacuum 
chamber; place any substance in the way of that beam, and X-rays will be 
produced.  The neat trick here is that while we can create an electron 
beam that always has the same energy, the energy of the X-rays depends on 
the substance.  Put a mixture of substances together, and a mixture of 
X-ray energies will be produced (and the brightness level at each energy 
corresponds to the proportions of the individual substances in the 
mixture).  This overall process is called "X-ray spectrometry".  There is 
a very nice stepped sequence of X-ray energies, corresponding exactly with 
the steps of discrete electric charges in atomic nuclei, from one in 
hydrogen to 92 in uranium.  When it was discovered that no substances 
seemed to exist which could provide X-rays of certain "missing step" 
energies, it could easily be deduced that unknown elements were waiting to 
be discovered.  For example, there is a group of elements known as the 
"rare earths", which range from Atomic Number 57 to 71, and which are so 
chemically similar that they are almost always found together in Nature.  
But place any sample of rare-earth ore into an X-ray spectrometer, and you 
will quickly see that Element 61 is missing!  And it stayed missing, 
despite considerable search, for decades.

When individual protons were discovered, everyone could acquire a 
reasonably simple picture of an average atom, and gain the fundamental 
rationale behind the Periodic Table of Elements.  Protons were locked 
together in the atomic nucleus; each proton electrically attracted one 
electron, which went into orbit about the nuclues.  (One mystery concerned 
the fact that the number of protons in an atomic nucleus did not add up to 
equal the Atomic Weight of that nucleus -- except in the lone case of 
hydrogen.)  Atomic orbits could hold multiple electrons, and naturally 
enough, the smaller inner orbits could hold fewer electons than the larger 
outer orbits.  Because protons in an atomic nucleus are very difficult to 
disturb, they ultimately control the total number of electrons associated 
with that nucleus.  This is why we use protons when counting Atomic 
Numbers; the association of an electron with an atom is often temporary.  
The chemical nature of an element is determined by the number of electrons 
in an atom's outermost orbit; chemical reactions are very often the cause 
of an electron's temporary association with a given atom.  (We can also 
use electical equipment to directly strip off electrons, so that the 
no-longer-electrically-balanced atoms become what we call 'ions'.)  
Chemically similar elements have the same number of outermost electrons.  
For example, sodium and potassium both have a single electron in their 
outermost orbit, but sodium has electrons residing in three different 
orbits, while potassium has electrons residing in four.  Rubidium, also 
similar with one outermost electron, has five orbits containing electrons. 
 (For the sake of completeness: hydrogen has just one orbit, lithium has 
two orbits, cesium has six, and francium has seven -- and all have just 
one outermost electron).  It must be repeated that the preceding is a very 
simplistic description; Quantum Mechanics was invented to provide a more 
accurate (but vastly more complex) description.  One complexity concerns 
the rare earth elements, which mostly have two or three electrons in their 
outermost orbit:  For these elements, as Atomic Number rises from 57 to 
71, the electrons are added to an INNER orbit, which for obscure reasons 
couldn't be filled any earlier.

When individual neutrons were discovered (having no electric charge, this 
was about as difficult as you might imagine), they provided the answer to 
the mystery of protons not adding up to equal an element's Atomic Weight, 
and they also provided the answer to such mysteries as why the Atomic 
Weight of chlorine is about 35-and-a-half.  There are two varieties of 
chlorine in nature, each having 17 protons in its nucleus, but one has 18 
neutrons and one has 20 neutrons.  So the total weights of these subatomic 
particles are 35 and 37; it happens that the variety of chlorine with a 
weight of 35 is significantly more common than the variety with a weight 
of 37.  Their average weight is thus 35.453, and this sort of variety in 
atoms goes under the name of "isotopes'.  The invention of a gadget known 
as the "mass spectrometer" has made it possible to identify all the 
isotopes of all the atoms in nature.  This device is a vacuum chamber 
permeated by a moderately strong magnetic field; a substance is introduced 
to the chamber in the form of an ionized beam.  As the beam passes through 
the chamber, the magnetic field causes the charged particles to follow a 
curved path.  The exact curvature depends on the speed of the particles, 
the strength of their electric charge, the intensity of the magnetic 
field, and, of course, the masses of the charged particles.  Two particles 
with the same charge but different masses, such as chlorine-35 and 
chlorine-37 with just one electron removed from each ('singly ionized'), 
will follow different curved paths through a mass spectrometer.  It was 
discovered that a lot of elements were mixtures of common and rare 
isotopes; one atom out of 600 of hydrogen, for example, has an Atomic 
Weight of 2 (its nucleus has a neutron accompanying the proton).  About 1% 
of carbon has a weight of 13, while the rest weighs in at 12.  Oxygen 
mostly exists in the form of isotope 16, but isotopes 17 and 18 exist 
also.  Many elements have only one isotope, such as fluorine, sodium, 
aluminum, and gold; some elements have quite a list:  tin holds the record 
with ten isotopes!

Physicists playing with neutrons soon discovered that lots more isotopes 
than the ones found in nature were (temporarily) possible; radioactivity 
is intimately associated with an imbalance of protons and neutrons in a 
nucleus.  It was discovered that ALL isotopes of Element 61 were 
radioactive!  Since the phenomenon of radiactivity is always associated 
with an atomic nucleus changing from one variety to another, all nuclei of 
Element 61 ever formed are doomed to disappear relatively quickly.  (It 
might be mentioned that Element 43 has the same problem.)

I guess that's enough, except for a few minor items.  Photography has been 
one other way to count particles, when used in conjunction with cloud 
chambers and bubble tanks:  look those up in a good encyclopedia.  And 
more recently, there are special gadgets used in large 
particle-accelerator laboratories to count obscure varieties subatomic 
particles; most of them are extremely complex and weigh many tons.  And 
finally, for further information, I highly recommend many of the 
nonfiction books written by the late Isaac Asimov.  Packed with names, 
dates, and events, he created an unequalled body of work describing the 
history of the development of Physics and Chemistry -- and he made it 
interesting, too!