Quantum Mechanics by Mandl Franz

Author:Mandl, Franz
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-06-03T16:00:00+00:00

6.1 ATOMIC STRUCTURE

In section 4.4.1 we specified the states of an atomic electron by atomic orbitals and described the states of a Z-electron atom in terms of configurations (n1l1)(n2l2)… (nzlz). We now want to assign angular momentum quantum numbers to atomic states.

6.1.1 Spectroscopic notation

First, I shall explain the standard spectroscopic notation. In it, one denotes states with quantum numbers L and S by 2S +1L, called a multiplet. 2S + 1 is called the multiplicity, and one writes S, P, D,… for L = 0, 1, 2, … . A 2S + lL multiplet comprises (2L + 1)(2S + 1) states corresponding to the values ML = L ,…, – L , Ms = S ,…, – S of the orbital and spin magnetic quantum numbers ML and Ms . For example, the carbon atom has the ground state configuration (1s)2(2s)2(2p)2. Since the electrons in the (Is) and (2s) shells have zero orbital angular momentum and are paired into singlet S = 0 states, the angular momentum of the atom stems entirely from the two (2p) electrons. We saw in section 5.7 that the (2p)2 configuration leads to multiplets 1S, 1D and 3P. To show from which configuration these multiplets stem, one would write (2p)2 1S [or more fully (ls)2(2s)2(2p)2 1S], etc. Combining L and S into a total angular momentum J , where

(6.1)

one denotes the states to which the multiplet 2S +1L gives rise by 2S+1Lj which is called a spectroscopic term (or just a term). For example, carbon has the ground state 3P0, i.e. it is an L = 1, S = 1 state with total angular momentum J = 0. For a single electron, one writes l , s, j instead of L , S , J , and combining its orbital angular momentum l with its spin s = gives a resultant angular momentum

(6.2)

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