16 June 2018 at 8:12 pm #574059
Why does sodium exist as a doublet and magnesium as a triplet in absorption lines of the Sun ?
Is this due to spin-spin coupling or the Zeeman effect ?
Attachments:18 June 2018 at 5:00 pm #579614Robin LeadbeaterParticipant
The two Na D lines are from the two different spin levels. (3s to 3p1/2 and 3p3/2 in absorption) There probably is Zeeman splitting of the lines as well but this will be very small in the solar magnetic field.
Robin18 June 2018 at 6:07 pm #579615Thomas KillesteinParticipant
Robin is correct, the splitting comes from the two 3p levels, which would be degenerate (i.e. no doublet) if not for the spin-orbit coupling – a sort of internal Zeeman effect from the magnetic field induced by the orbiting electron. This splits the levels and creates the doublet. If we apply a weak magnetic field (similar in size to the spin-orbit bit) we’ll get Zeeman splitting of these levels and end up in turn with 10 lines (5 from each line of the doublet)
The Na triplet is more complicated, but I think this comes from a similar 4s -> 3d transition, and selection rules exclude some of the 5 sublevels of the 3d orbital, giving a triplet – I’m slightly less clear on this one.
Tom18 June 2018 at 8:09 pm #579616Andrew SmithParticipant
If you go on the NIST spectral data base and look at the relevant lines it shows you the transitions involved.
As above the splitting is due to the spin orbit coupling of the magnetic moments.
Regards Andrew19 June 2018 at 8:47 pm #579620
Robin, Thomas and Andrew,
Thank you for your answers, its become much clearer what’s going on and why.
Essex UK21 June 2018 at 6:49 pm #579633Andrew SmithParticipant
It might be worth pointing out that the H alpha line is made up of 7 components with two being significantly stronger than the others. The splitting is small withthe largest spin orbit coupling split in the 2p level (J = 3/2 ,1/2)
The theory of the spectrum of the Hydrogen atom traces the development of the quantum theory of light and matter. From the Bohr model where all the lines are degenerate in the prime quantum number (as the are in the Schrodinger model) through the development of Sommerfeld and Schrodinger to the relativistic theory of Dirac, Darwin, Lamb and on to QED for which Shin’ichirō Tomonaga, Julian Schwinger and Richard Feynman got the Nobel prize building on the work of many others, where they are all split apart.21 June 2018 at 11:56 pm #579634
Thanks for your input.
I never knew the h alpha line has 7 components.
Also a good point about the development of the quantum theory of light. No one person invents anything. In another example, Edison alone did not invent the light bulb, he needed Franklin’s work on electricity nearly 200 years before him.
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