Lecture Notes from CHM 1341
13 June 1996

ATOMIC STRUCTURE

For chemists, the fundamental units of matter aren't the quarks of which all fundamental particles are composed; that's because chemical reactions cannot generate the energies necessary to disrupt atomic nuclei let alone their constituents! Chemists are keenly interested instead in ELECTRONS which bind atoms together into molecules, PROTONS which attract electrons into atoms, and NEUTRONS which stabilize the heavier nuclei.

It turns out that there is an atom which contains exactly one each of these particles; it is the deuterium atom, called "heavy hydrogen" because normal hydrogen atoms lack that neutron. Indeed, the mass of atoms resides almost entirely with the near equally heavy protons and neutrons. The electrons are almost 2000 times lighter than either. However, electrons are formidably important because they each carry a negative electric charge equal (but opposite) to the positive charge on each proton. The NEUTRon, as one might suppose, is electrically neutral.

That deuterium doesn't appear explicitly on the Period Table prompts us to mention that each uncharged element is unique in its chemical and physical properties as a function of the number of protons (and, since it's uncharged, equal number of electrons). Adding or subtracting neutrons appears only to destabilize the nucleus of the atom. So, for example, although another ISOTOPE of hydrogen (called tritium) is know which adds yet a second neutron, it is so highly radioactive that it is never found in Nature except as a shard of the demolition of some other nucleus. But deuterium is sufficiently abundant to influence the average mass of hydrogen in its 3rd decimal place.

The use of the word NUCLEUS implies a kernel at the heart of an atom, and that "nucleus" is the location of all the protons and neutrons...and thus of all the mass. Rutherford and others were astounded to discover that convenient nuclear bullets (they used helium nuclei, known as "alpha" particles) would occasionally bounce straight back from a gold foil pounded so thin that the vast majority of alphas just breezed straight through as if it weren't there! (Gold is one of the few metals which is so "malleable" as to be flattened that thin without coming apart.) Those richocheting alphas were signalling a hard nut (kernel) at the core of each Au (gold) atom. Since the alphas were positively charged like the protons, elementary charge-scattering equations showed that nucleus to be 10,000 times smaller (in radius) than the atoms...or more precisely, than the space between the atoms.

The 2000 times lighter electrons were no match for the alphas. Helium nuclei have 2 protons + 2 neutrons, so they're 8000 times heavier than an electron! Thus was born the notion of the atoms as tiny cores of mass with virtually empty space between them occupied by whispy electrons. Fortunately, those whispy electrons repel one another so effectively that the infinitesimal nuclei cannot collapse upon one another.

Chemical elements are often written as atomic symbols without regard to the number of different isotopes they might represent given small variations in the number of their neutrons. Instead, chemists just use the isotope-averaged atomic mass in their calculations, confident that the isotopes are sufficiently stable to last well through the history of any chemical experiment. This turns out to be wildly successful unless one insists on discovering the chemistry of very heavy atoms indeed whose isotope lifetimes are measured in less than a minute. Not only must precautions against radiation have to be taken but also experiments must be designed to conclude in seconds after these behemoths are created in nuclear accelerators.

However, when it becomes important to discriminate between the isotopes of an element, as in recognition of their differing nuclear properties (such as response to varying magnetic fields in medical Magnetic Resonance Imaging), then chemists borrow the scheme from physicists which augment the element symbol with super- and sub-script numbers PREFIXed to the symbol...the ordinary suffix positions for super- and sub-scripts are already reserved for ionic charge and combining numbers in molecules. If the number of an elements protons is Z, and the number of the sum of protons + neutrons (containing virtually all of the atom's mass remember) is A, then an element like chlorine (Cl), for example, might be more carefully described as either

35      37                A
  Cl or   Cl representing  {symbol}
17      17                Z

since it always has 17 protons but 75% of Cl atoms have 18 neutrons while 25% possess 20 neutrons! The weighted average atomic weight would be 0.75*35+0.25*37=35.5 which is what's recorded on the Periodic Table for chlorine's NATURAL ABUNDANCE weight. These naturally averaged atomic weights can be safely used because in doing chemistry with bulk materials, the number of atoms is staggering. Any experiment with individual chlorine atoms, however, would find every 4th one to be two atomic units heavier than the others. Since protons and neutrons are almost identically massive, it makes sense to define an atomic weight with their sum. Since very many atoms take part in bulk chemistry, it makes sense to use their isotope-averaged atomic weights.

There's a dark tale of once when that was an inappropriate choice. During the Cold War, hydrogen bomb stockpiles used so much of the A=7 isotope of lithium that chemists noticed that their laboratory stocks of compounds containing lithium no longer had the natural abundance weight!

So the standard atomic mass can be set with some convenient isotope which is readily obtainable and separable from its brethren. (Isotopes can be separated by their mass differences in spectrometers or diffusion apparatus or more modern laser beams tuned to discriminate slower vibrating atoms from quicker ones.) The standard of choice is

            12
              C
             6

and the UNIT mass is calculated as 1/12 of that to define u=1 amu (atomic mass unit), the weight of an element with A=1. Notice that Gillespie's Table 1.4 shows atomic masses to 6 or 7 significant figures; they're known that accurately from mass spectrometry which measures the bending of charged atomic paths by a magnet; more massive nuclear, having more inertia, follow less bent trajectories. So atomic weights are very well known. Unfortunately, the magnitude of this atomic mass unit,

            u = 1.6605 x 10-24 grams

is not at all convenient for bulk chemistry! We'd rather be dealing with a whole gaggle of atoms, N, so large that N*u is 1 gram. Well, the algebra is terribly simple...just invert

        1 gram per gaggle 
N = ----------------------------- = 6.022 x 1023 particles per gaggle
    1.6605 x 10-27grams/particle

But "gaggle" is a collection of geese not atoms. This particular number of particles is called AVOGADRO'S NUMBER instead.

      NA = 6.022 x 1023 particles = 1 mole of particles

Now we can interpret the chemical reaction symbolism as telling us that not only does 1 glucose molecule react with 6 oxygen molecules

      C6H12O6(s) + 6 O2(g) -----> 6 CO2(g) + 6 H2O(l)

to produce 6 each of carbon dioxide and water molecules, but one MOLE of glucose will produce 6 MOLES of carbon dioxide as well, for example. Since we can readily calculate the molecular weight of glucose from the atomic weights of each of its elements conveniently listed on the Periodic Table and do the same for all of the other molecules in that reaction, we then can know how much carbon dioxide we have to exhale for each gram of glucose we ingest. It's easy: if (a mole of) glucose weighs 6(12)+22(1)+6(16)=190 grams, and it produces six moles of carbon dioxide weighing 6 times (12)+2(16)=44 grams or 264 grams, then elementary ratios tell us the 1 gram of glucose will cause us to exhale (264/190)=1.39 grams of carbon dioxide. Exhaling more than you ingest sounds like magic until you realize that you INHALED the oxygen which combined with the glucose too!

It isn't really fair to say that chemists ignore nuclei which aren't stable. In fact, they use them to track down where atoms go in chemical reactions. For example, it's clear that the hydrogens in the water made when glucose burns can only have come from the glucose itself, but the oxygen atoms in that water might have come from either glucose or the molecular oxygen or both. One could discover that by "labeling" the oxygens in glucose with the A=17 isotope instead of the A=16 one and testing for ¹⁷O in the products. So some knowledge of isotopes and their decay schemes (how their unstable nuclei fall apart) is of advantage in the field known as Radiochemistry.

To a very good approximation (Einstein notwithstanding), both mass and charge are conserved in the decay of nuclei. Most schemes involve splitting unstable nuclei into only slightly different ones with the release of either "alpha" particles (helium ions) or "beta" particles (electrons). The nuclear decay reactions are written just like chemical reactions except that the A and Z notations are included. Since we can't balance atoms when they are not conserved, we must balance A and Z instead...that's nuclear physics grammar/syntax/semantics! So uranium (U) decays to thorium (Th) by ejecting an alpha particle (He), but the thorium goes on to kick out a beta particle (electron) to become proactinium (Pa) like:

   238          234       4
      U  ----->    Th  +   He
    92           90       2

   234          234       0
      Th ----->    Pa  +   e
    90           91      -1

Notice that the sum of the Zs on the right always equal the Z on the left? Likewise with the As? So if you didn't know it was a BETA particle released when thorium decayed to proactinium, you could deduce it by the deficits in A and Z in the absence of the beta!

Chris Parr
University of Texas at Dallas
Programs in Chemistry, Room BE3.506
P.O. Box 830688  M/S BE2.6 (for snailmail)
Richardson, TX  75083-0688

   Voice: (214) 883-2485
     Fax: (214) 883-2925
     BBS: (214) 883-2168 (HST) or -2932 (V.32bis)
Internet: parr@utdallas.edu  (sends Chris e-mail.)