By B. Pebay-Peyroula, J.-C. Cagnac
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Extra resources for Modern Atomic Physics: Quantum Theory and Its Applications
H-, defining the components of the electron spin. The Pauli principle is a consequence of the indistinguishability of electrons and has been incorporated already in proposition (2) set out in the preceding section. It may be stated as follows: in an atom, the wave functions of the individual electrons must all be different from one another, and two electrons therefore cannot have identical values for the set of four quantum numbers n, I, mz, m•. This principle turns out to have fundamental consequences in the physics of the atom.
To avoid confusion later, we shall no longer denote the magnetic quantum number, related to the orbital angular momentum, by m, but instead by m1 with the subscript I. To summarise, the electron in the atom will therefore be characterised by the four quantum numbers: n, the principal quantum number; I, the quantum number defining the orbital angular momentum; mz, defining the components of a 1 along the axis of quantisation; m. = H-, defining the components of the electron spin. The Pauli principle is a consequence of the indistinguishability of electrons and has been incorporated already in proposition (2) set out in the preceding section.
Example For a system with three electrons, we may readily find the following orders of degeneracy the configuration ls2s2p --:. G = 2 x 2 x 6 = 24 2p3d4f --:. G = 6 X 10 X 14 = 840 Second case: several electrons in the same sub-shell. Consider a configuration in which X electrons possess the same n and I quantum numbers. For this value of/, an electron can have Y = 2(2/ + 1) different states characterised by different values of m 1 and m•. To enumerate the number of possible states, we must take account of the Pauli principle and of the indistinguishability of the electrons.