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5112 2013-8-18 01:05 PM

electron transition and angular momentum

transition from s orbitals can only involve p orbitals because photons carry angular momentum (from my lecture notes).
is it because the photon that strikes out the electron from s orbital carries angular momentum, by conservation of momentum, electron must be transitted according to this angular momentum and filled into either x,y,z axis of p orbital?

as d orbital carries different angular momentum as well, is it possible for electron from s orbital be transitted into d orbital by the same principle that involved in s-->p orbital electron transition?

thanks at all

jmlo 2013-8-18 02:27 PM

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[quote] transition from s orbitals can only involve p orbitals because photons carry angular momentum (from my lecture notes).
is it because the photon that strikes out the electron from s orbital carries angular momentum, by conservation of momentum, electron must be transitted according to this angular momentum and filled into either x,y,z axis of p orbital? [/quote]
This is an explanation for the Laporte selection rule in atomic spectra. Due to the conservation of angular momentum, when a photon, which has an angular momentum of 1, is absorbed, then the excited electron should have an increase of orbital angular momentum of 1. Similarly, when a photon is emitted, the de-excited electron should have a decrease of orbital angular momentum of 1.

However, note that this account does not reflect the actual origin of the observed selection rule, despite making complete physical sense and being easily understandable. Recall what we have learnt in the quantum theory of atoms. The transition of an electron between two energy levels is dictated by the transition moment integral (I presume you have learnt this from your physical chemistry class, haven't you?). By group theory, a non-zero integral results when the transition dipole integral belongs to the totally symmetric representation of the atom. This restriction is fulfilled for atoms if the initial state and final state are of opposite parity.

To put it in a more general way, it means that the transition dipole moment integral is not zero (or in other words, a non-zero probability of transition) if the electron jumps between two orbitals whose symmetry is different. Why is s ---> p transition possible? It is better seen by drawing the 3D shapes of s and p orbitals of an atom. The s orbital is spherical which has no inversion centre. On the other hand, the p orbitals have inversion centre at the origin (i.e., it changes sign when going from one end to the other). It means that the s and p orbitals are of opposite symmetry, and thus the transition dipole moment integral is not zero.

[quote]  as d orbital carries different angular momentum as well, is it possible for electron from s orbital be transitted into d orbital by the same principle that involved in s-->p orbital electron transition? [/quote]
No, this transition is not possible under usual conditions. There are two reasons. Firstly, since both s and d orbitals have no inversion centre, they are of the same symmetry, and thus the resulting transition dipole moment integral is always zero. Secondly, if you look at the details of the calculations of transition dipole moments, you will see that the Laporte selection rule based on quantum mechanics states that the allowed change of orbital angular momentum is +/- 1. As the s orbital has l = 0 while the d orbitals have l = 2, the transition between these orbitals is not allowed.
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