PHYS-115 (4) Kaldon Spring 2005Atomic and Nuclear PhysicsAll models of the atom are fundamentally wrong –that’s one way to think about the topsy-turvy world thatquantum mechanics brings to physics. It’s simplest to thinkabout atoms like this: You’ve got a nucleus which consistsof positively charged protons and neutral neutrons,surrounded by orbiting negatively charged electrons. Anatom, by the way, has the same number of electrons asprotons. If we have more (or fewer) electrons, we call theatom an ion. The Bohr Model of the atom makes theseelectron orbits be circular, and it looks kind of like aminiature solar system. Probably the classic “picture” ofthe atom has the electrons whirling around the nucleus inall directions. In truth, the electrons are subject to a specialkind of physical law that deals more in probabilities thanabsolutes – we say (in the biz) that the electron is smearedaround the atom in a cloud, where the most probable places we mightfind the electron are represented by thicker cloud wisps thanelsewhere. But all of these models have to have some grounding inreality, and one of the realities of quantum mechanics is that theenergy of the electron orbitals is quantized, or only allowed to havespecific values, which depend on the type of atom and how many otherelectrons happen to be around at that time. If all the electrons are inthe closest orbits to the nucleus that are allowed for that atom, then theelectrons are said to be in the ground state. If energy is added to aground state electron by the absorption of some energy, it is said to bein an excited state. If an excited stateelectron gives up some or all of its extraenergy, which it can by emitting a photon (or particle) of light. Aparticular photon has onlyone color of light, and so wecan look at the series ofcolors of light coming from aparticular type of atom as akind of fingerprint for thatatom called a spectrum. Itwas these spectra that helpedestablished what the elementswere, and how we canidentify them. Helium, forexample, was first discovered in the spectrum of our Sun, asa series of lines leftover by identifying all the other spectrallines as belonging to known elements. Now, let’s go backto those ground state electrons. You can’t stuff all the electrons into the closest orbit – the PauliAtomic and Nuclear Physics Handout PHYS-115 Page 2Exclusion Principle states that no two electrons can exist in the same exact state at the sametime. So every electron has to be different in some way. The quantum number n tells you howbig the radius of the orbit is; so the innermost orbital is for n = 1. You can have two of these n =1 electrons, because the are said to have spin in the opposite direction, spin up or spin down.These n = 1 electrons are in spherical orbits, or s-orbitals, so we can call them 1s electrons. Forn = 2 electrons, you can have two 2s electrons, but you can also have electrons in orbitals thatmove in teardrop shaped clouds, thatpoint in the x, y or z directions –these are the six 2p orbitals. Youdon’t have to memorize all thesenumbers to learn that the fact thatthere are such numbers dictated bythe rules of quantum mechanics thatdetermines the shape and order ofthe Periodic Table of the Elements.And so also all of chemistry.Elements are determined solely bythe number of protons in the nucleus. An atom or ion that has one proton in the nucleus is theelement Hydrogen, irrespective of how many (or how few) electrons are in orbit around thatnucleus. Two protons in the nucleus is Helium, three protons is Lithium, etc. In the pre-NuclearAge Periodic Table, there were 92 naturally occurring elements; Hydrogen to Uranium.(Technetium (43) isn’t found in Nature, but Plutonium (94) probably is.) Since then, we haveexpanded the Periodic Table to include another 18+ man-made elements, some of which mayactually occur in Nature, but in very small amounts.In all of this discussion we have not said anything about the neutrons in the nucleus.That’s because they have nothing to do with the arrangement of the elements in the PeriodicTable or in the determination of what the electrons do in Chemistry. The neutrons are there forthe sake of the nucleus, and are therefore the domain of Nuclear Physics, not Chemistry. (Okay,there is a field called Nuclear Chemistry – let’s not quibble.) So what are those neutrons doinganyway? They don’t have an electric charge like the electrons and the protons – and that’sexactly the point. Without the neutron, there would be only one element possible: Hydrogen. Tomake Helium, you need two protons. But the protons repel each other, and at the tiny distancesacross the nucleus (10-15 m or 0.000 000 000 000 001 m or 1/100,000th the size of the electronorbitals!) they repel each other really fiercely. The Force between two protons in the nucleus isabout 230 N – that’s the same Newtons we were using before, and it’s equivalent to the weightof a 52 pound object!!! But neutrons are attracted to protons through the strong nuclear force,which is a force that exists only in the short distances of the nucleus, and it is really strong. Soyou need to add some neutrons (not too many, not too few) in order keep the nuclei of all theother elements together, but there is not just one value for N, the number of neutrons, to go withZ, the number of protons in each elements. And that means that there are isotopes, elements thatare the same chemically, but have different nuclei, with different numbers of neutrons. So thereis not just one value for A = Z + N, the atomic weight. The atomic weights that are listed in thePeriodic Table are actually an average value – based on the usual ratio of isotopes of a particularelement in naturally occurring samples of the elements. You can usually make a good guess ofwhat A is for the most common isotope, by rounding the atomic weight in the Periodic Table to aAtomic and Nuclear Physics Handout PHYS-115 Page 3whole number and subtracting the proton number, Z. For example, Gold is Au (from the Latin,aurum). It has an atomic number of 79 and an atomic weight of 196.9665. If you panned forgold in the streams of California, and accumulated 1 mole of gold atoms (1 mole of anything isone Avogadro’s Number of anything; Avogadro’s Number, NA = 6.02 × 10²³) then it would havea mass of 196.9665 grams (which is 0.1969665 kg or, on the surface of the Earth, it would have aweight of