Selection Rules and Atomic Spectra

The selection rules for atomic spectra are determined in the same way as it was done previously for vibration-rotation spectroscopy (see Section 6.7). For a hydrogen atom, the dipole moment operator of the incoming photon, H, is operated on and integrated over all space between the initial state n, /, m, with the final state n , m/ . Allowed transitions occur when the integral 

The selection rules in terms of / and m/ have been determined previously for the vibration-rotation of a molecule (recall that the wavefunction for a hydrogen atom is in part the spherical harmonics, R /Y/ ) by simply replacing the J for an / and Mj for an m/ in Equation 6-84. 

The integral in Equation 8-72 in terms of the radial component is considerably more difficult to solve. The result of the integration is that any An is allowed. 

The various lines seen in an emission spectmm are named by their discoverers or principal investigators and are shown in Table 8-3. 

In the case of a hydrogen atom, aU of the states are doublets, hi the case of multi-electron atoms, there may be different spin states. For light elements where the spin-orbit coupling is weak, the selection mles are as follows. 

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