@Eagle Mum, you are correct that the sodium D lines correspond to a transition between the 3s and 3p orbitals and it is this transition that is responsible for the flame test colour and the yellow sodium vapour lamps.
However, the fact that sodium atoms in a vapour lamp have an excitation from the 3s to the 3p orbital and the subsequent reverse transition leads to the emission does not mean that the excitation must have been an electron from the 3s orbital of a ground-state uncharged sodium atom to its 3p orbital.
1. Both an uncharged sodium atom and a sodium cation will give a yellow colour in a flame test
The selection rules for symmetry-allowed and symmetry-forbidden transitions in electronic spectroscopy are determined by the transition moment integral:
Specifically, if the transition moment function,
is antisymmetric (that is, the function is odd) then the integral is zero and the transition is forbidden. If the wavefunctions relate to a species that has an inversion centre then the transition moment operator
for an electric dipole transition has
u symmetry and so is odd (recall:
u is an abbreviation for
ungerade, the German for "odd"). Then, any transition in which
and
have the same symmetry will yield a triple product that is odd and a transition that is symmetry-forbidden. Both a single uncharged atom of sodium (or any other element) and a monatomic ion are spherical species and thus have an inversion centre. Consequently, in these species, transitions between orbitals of the same type of sub-shell are symmetry-forbidden as the excited and ground state wavefunctions will have the same symmetry, whether that be
u symmetry of a p orbital or the
g symmetry (
g = gerade, "even") of an s or d orbital.
In other words, quantum mechanics dictates that transitions s to s, p to p, d to d, and f to f, are all forbidden on symmetry grounds in a spherical species. An excitation of an electron in a 2p orbital in a sodium cation is thus most likely to be 2p to 3s or 2p to 3d. An excitation from an already-excited sodium cation with a 3s electron is most likely to be 3s to 3p. The only possible relaxation pathway for an excited state sodium cation with a 3p electron is 3p to 3s unless there is (somehow) a vacancy in a 2s or 1s orbital. An excited state sodium cation with a 3d electron can relax 3d to 3p or 3d to 2p but not 3d to 3s.
In reality, spin-forbidden transitions are not necessarily impossible because vibrational coupling can alter the symmetry sufficiently for them to become weakly allowed, but that is not important in this case. Also, since these selection rules apply equally to a sodium atom as they do to a sodium cation, nothing in the above prevents uncharged sodium atoms present in a flame from producing a yellow colour - in fact, if uncharged sodium atoms are present, they will produce a colour. What the rules do explain is why sodium cations will also produce a yellow colour if present in a flame - though there is no 3s electron in the ground state, that does not mean that excitations can't be 2p to 3s to 3p and reverse, to give the flame colour, with an alternative being a 2p to 3d excitation with a 3d to 3p to 3s to 2p relaxation pathway.
2. Could we have uncharged sodium atoms in a flame?
If there is sodium vapour around, as in a sodium vapour lamp, sure. If there is sodium metal around, also sure - metallic sodium melts at 98 degC and boils 883 degC, so a bunsen is easily hot enough to turn Na(s) into Na(g). However, sodium metal oxidises rapidly in air and sodium oxide (Na
2O) melts at 1132 degC and sublimes around 1275 degC. Even if sodium metal is present, placing it into a flame with an ample supply of air guarantees it will become sodium ions as part of an oxide rapidly.
For a flame test with sodium chloride, the question that
@dumNerd asks is, for me, critical... if sodium chloride were somehow producing uncharged sodium atoms in a flame test, where is the electron coming from to reduce the sodium cation?
2 Na
+ + 2 Cl
- -----> 2 Na + Cl
2 might seem plausible at first, but:
- the reaction as written has an E0 ~ -4 V and so would require very forcing conditions
- the reaction is highly endothermic, deltaH ~ +820 kJ mol-1
- chlorine gas is pretty noticeable
- sodium metal burns in a chlorine environment to make NaCl, so why would we expect the reverse to happen in a flame?
- sodium chloride is a highly stable ionic substance, melting point 800 degC, boiling point 1465 degC
If the flame test is done with some dissolved NaCl, the flame will vapourise the solvent and release solvated ions (like [Na(H
2O)
6]
+) in gas state into the flame where the heat will strip the coordinate water molecules and reveal a bare monatomic sodium cation. Even the octahedral complex (which is centrosymmetric and thus subject to the same selection rules) will emit yellow light from a 3p to 3s transition from the relaxation of any electrons that are promoted to the 3p subshell. Vapourising the solvent can also lead to formation of solid NaCl as the solubility limit is reached and the heat will be sufficient to liberate some ions from the solid (in the same sort of way as water evapourates at below its boiling point).
In short, the sodium cation is much more stable than sodium metal because the latter is easily oxidised to the former, even in air at room temperature. In a high-energy environment like a flame, short-lived and unstable species can be formed but it is difficult to see how or why sodium cations would be reduced unless something even more readily oxidised were present - and any such would surely be oxidised by air long before a sodium cation was encountered.
3. Summary
- Though the selection rules and related mathematics are well beyond HSC level, the conclusion they support is not too complicated. Whether it be an excited state sodium cation or uncharged sodium atom, once an electron is excited into the 3p subshell, its only (reasonable) relaxation pathway is via the emission of yellow light whose wavelength corresponds to the gap between a 3p and the 3s orbital.
- Explaining how a flame test using a sodium compound can come to introduce sodium cations into a flame is straight-forward. It is difficult, however, to conjecture a plausible chemical explanation for those cations being reduced to produce uncharged atoms of sodium metal in a flame.
- Personal Recollection: I recall doing experimental work in my undergraduate chemistry studies of the spectroscopy of flames, looking for evidence about the short-lived intermediates from combustion that can be detected in that environment. The molecule C2, for example, can be detected easily and its spectroscopic properties used to calculate its bond strength and bond order. I remember my surprise that the two most intense transitions we detected in the blue flame of an ordinary bunsen burner were the D lines of sodium. The lecturer in charge explained that these are caused by salt in the air that deposits onto the inner walls of the bunsen burner itself. The lines have such great intensity that they are observable even when only a tiny amount of sodium is present, and I learned from it that salt contamination is something to bear in mind in some types of spectroscopy.