all s have the same value of α regardless of n. Where α has a particular value for each value of l, e.g. The problem with the latter is that, owing to orbital penetration (the same effect that causes the energy to rise from s to p to d), the energy levels have to be modified by an empirical term, the quantum defect, α. However, it is more difficult to guess the starting value of m for transitions between high values of the principal quantum number and much more difficult to guess for non-hydrogenic atoms. If the guess is correct a graph of line wavenumber against 1/ m 2 will give a straight line and the intercept at 1/ m 2 = 0 ( m = ∞) gives the ionization energy of the fixed level. For hydrogen and hydrogen-like atoms it is often easy to guess the starting number of the m series. A given series of lines involves one fixed energy level and a set of levels with a succession of principal quantum numbers, the wavenumber ( cm -1) being given by the equation The assignment of the correct values of the quantum numbers to the lines in an atomic spectrum requires an approach of a type that you have not come across before. (vi) Application of the results to the understanding of the periodic table. Russell-SaundersĬoupling of L and S to give the total angular momentum (v) The coupling of spin and orbital angular momentum. You can observe the atomic spectrum of sodium in the work for a second year tutorial on electronic spectroscopy. A program that simulates the spectra of the alkali metals and other elements is used below to calculate the spectra of lithium and hydrogen. The physical origin of theĭoublet structure in the alkali spectra. Of inner electron shells by the outer electrons. The effect on the energy levels of penetration (iii) Electron spin and the Pauli principle. The selection rules for l in determining the spectrum. The angular wavefunctions and space quantization of the angular momentum. Shape of wavefunctions with different values of l. (ii) The nature of the wavefunctions of the hydrogen atom, especially theįorm of the radial wavefunction. The ionization potential from the line spectrum. Of the levels in terms of the Bohr model of the atom. Their relation to the energy level diagram (Grotrian diagram). The Thomas Group - PTCL, Oxford Atomic Spectra - 1st year
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