Let's now see how electrons spin, explains why the number 2 crops up in the phenomena we've mentioned. Pauli proposed the exclusion principle. In video 6 we labeled hydrogen orbitals by 3 quantum numbers, N, L, and M, or as we'll call it from now on, M sub L. In this video we've seen that an electron also has quantum numbers S and M sub S. N can have values 1, 2, 3, etc. and specifies energy. L can have values 0, 1, 2, up to N minus 1 and specifies angular momentum magnitude. M sub L can have values of minus L, minus L plus 1 and so on, up to L and specifies the z-component of angular momentum. S is equal to 1,5, and specifies spin angular momentum magnitude. Finally M sub S can have values of minus 1,5 or plus 1,5, and specifies the z-component of spin angular momentum. Pauli's exclusion principle states that only a single electron can occupy a quantum state specified by the four quantum numbers N, L, M sub L, and M sub S. We don't bother listing S since that's fixed at 1,5 for all electrons. So, an orbital with given values of N, L, and M sub L can hold 1 electron with M sub S equals 1,5, and 1 electron with M sub S equals minus 1,5. That is, each orbital can hold 2 electrons. Now, by simply filling up each orbital with spin up and spin down electrons, we naturally arrive at the sequence of numbers 2, 8, 18, and 32 that characterize the periodic table. The mystery of that factor of 2 is now been solved, and a new physical principle, the exclusion principle, has been discovered. Now, we turn to the fine structure of atomic spectra. In video 7, we discussed how the orbital angular momentum of an electron should create a magnetic dipole. Consider how this will interact with the dipole created by the electron's spin. The electron can be spin up that is the two dipoles are more or less parallel, or it can be spin down with the dipoles more or less anti-parallel. The interaction of these dipoles is called spin orbit coupling. Since like magnetic poles repel, in the parallel arrangement, the repulsion of the dipoles will result in relatively higher energy. In the anti-parallel arrangement, the attraction of opposite poles will result in a relatively lower energy. So, we would expect two energy levels corresponding to the two possible electron spin orientations. A detailed analysis of this effect shows its characterized by the so-called fine structure constant alpha, which is approximately 1 over 137. The fractional energy shifts are on the order of alpha squared, which is about 50 parts in a million, the same order of magnitude is observed in the fine structure of atomic spectra. Also, note that if the electron is in an s orbital with no angular momentum, then the orbital angular momentum dipole will be absent, and there should be no spin orbit coupling and no fine structure splitting. And this is indeed what we observe. Finally, let's consider the Fipps Taylor and Stern Gerlach experiments, in which beams of neutral atoms are split into two by a non-uniform magnetic field. In its ground state, the 1 s orbital, the hydrogen electron has no orbital angular momentum, but it does have spin angular momentum, which can take on two orientations. The resulting two orientations of the spin magnetic dipole mean that a beam of hydrogen atoms will split into two in the presence of a non-uniform magnetic field. With 47 electrons, the silver atoms used in the Stern Gerlach experiment are more complicated. It turns out that 46 of them are arranged in so-called filled shells, which have no net orbital or spin angular momentum. So this leaves a lone electron in a 5 s orbital, which, like the hydrogen electron, has no orbital angular momentum, but does have spin angular momentum. The two components of this lead to the two spots seen in the Stern Gerlach experiment. In classical physics, the concept of conserved quantities, most notably energy, linear momentum and angular momentum, are of immense importance. These conservation laws are not immediately obvious, and they require long periods of experimental and theoretical work to establish. Now, we've seen time and again that, in quantum physics, classical concepts are not necessarily valid. Therefore, we shouldn't simply assume that energy and momentum are conserved in the quantum realm. So far, we've seen that conservation of energy does appear to apply to atomic scales. The energy lost by an atom in the transition between quantum states is transferred to an emitted photon. Likewise, the linear momentum carried by photons allows a consistent picture of linear momentum conservation in quantum mechanics. But what about angular momentum? Quantum mechanical spin doesn't even correspond to any classical phenomenon. Therefore, it seems conceivable that angular momentum may not be conserved at the quantum level. Let's take a look at this. In video 6, we saw that combining stationary states of different energies, orbitals, creates an oscillating electron probability distribution. If this oscillation effectively forms a good radiating antenna, a so-called electric dipole, then it's possible to transition between these two orbitals by the emission or absorption of a photon. If the oscillation does not have this electric dipole characteristic, then single photon transitions between these orbitals will not occur. Calculation of these electric dipole transition probabilities leads to the so-called selection rules for hydrogen atom radiation. An orbital with quantum numbers n1, l1, ml1, and ms1 can transition to an orbital with quantum numbers n2, l2, ml2, and ms2. Only if l2 differs from l1 by plus or minus 1, ml2 equals ml1, or differs from it by plus or minus 1, and the spin quantum number does not change. The quantum number l fixes the orbital angular momentum magnitude. If the spin angular momentum doesn't change, but the orbital angular momentum does change, then the total angular momentum of the atom must change. In the situation we just animated, an orbital with n equals 2, l equals 1, and ml equals 0, can emit a photon and transition to an orbital with n equals 1, l equals 0, and ml equals 0. The initial state has orbital angular momentum of magnitude square root of 2h bar. In the classical picture, the electron is going around the proton. The final state has no orbital angular momentum. Classically, the only motion available to the electron is directly toward or away from the proton. If angular momentum is conserved at the atomic level, then where did the angular momentum of square root of 2h bar go? There seems to be only one possibility. The photon. The photon must carry angular momentum of magnitude square root of 2h bar. Since the photon is a single particle, this is presumably a spin angular momentum. Apparently, photons carry an intrinsic angular momentum. Photons are particles with spin s equals 1. In 1931, Shandrushakara Rahman and Suri Bhagavatam presented experimental evidence that the photon does indeed carry spin angular momentum. Photons, like electrons, have spin. Do they also obey the exclusion principle? In video one, we talked about the modes of an electromagnetic field inside a box. These modes are photon quantum states, and they can contain an arbitrary number of energy quantum, that is, any number of photons. There is no exclusion principle for photons. In fact, electrons and photons are members of the two families to which all known particles belong. Particles with half-inager spin, such as the electron with spin 1 half, are fermions, named after Enrico Fermi, and obey the exclusion principle. Particles with integer spin, such as the photon with spin 1, are bosons, named after Satyendra Nath Bose, and do not obey the exclusion principle. The properties of all currently known particles are described by the standard model of particle physics. The electron is among the fermions, on the left side of the vertical dotted blue line, all of which have spin 1 half and make up the material of our day-to-day world. The bosons are on the right side. The particles in the orange column, which includes the photon, have spin 1 and are responsible for carrying the strong and weak nuclear forces and the electromagnetic force, which govern the interactions of the fermions. Finally, the recently confirmed Higgs boson has spin 0.