Transcript Spectroscopic Observations

Spectral Line Physics
Atomic Structure and Energy Levels
Atomic Transition Rates
Molecular Structure and Transitions
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Quantum Numbers
(http://www.ess.sunysb.edu/fwalter/AST341/qn.html)
• n, principal quantum number. Defines the distance of
the electron from the nucleus in the Bohr model.
• l, the azimuthal quantum number. l takes on the
integral values 0, 1, 2, ... , n-2, n-1. Defines angular
momentum.
• m, the magnetic quantum number. m takes on the
integral values -l , -(l-1), ..., -1, 0, 1, ..., (l-1), l.
• s, the spin quantum number. This describes the spin
of the electron, and is either +1/2 or -1/2.
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Quantum Numbers
• Pauli exclusion principle: no two electrons have the
same set of the 4 quantum numbers n, l, m, s
• There are 2n2 possible states for an electron with
principal quantum number n (statistical weight).
• The n=1 levels can contain only 2 electrons. This level
is called the 1s orbit or the K shell
(shells with n=1,2,3,4,5,6,7
are called the K, L, M, N, O, P, Q shells, respectively).
• An orbit, or shell, containing the maximum number
2n2 electrons forms a closed shell.
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Energy levels for n = 3
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Quantum Numbers for Atoms
• l =0, 1, 2, 3,4
s, p, d, f, g
• total orbital ang.
mmt. for multielectron systems
L =0, 1, 2, 3,4
S, P, D, F, G
• S is total spin
• J=L+S is the total
angular mmt.
(2J+1) degenerate levels for each J unless
magnetic field applied (Zeeman splitting) or
electric field applied (Stark effect).
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Spectroscopic Notation
• The atomic level is described as n 2S+1LJ
where S, n, and J are the quantum numbers,
and L is the term (S,P,D,F,G, etc.).
2S+1 is the multiplicity.
• Ground state of Boron: 1s22s22p1
configuration, with 2 e- in the n=1 level (l=0), 2
e- in the n=2, l=0 s orbital, and last e- in the 2p
orbital.
The ground state of Boron has a 2P1/2 term.
• Closed shells always have a 1S0 term.
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Selection Rules (Electric Dipole):
Permitted and Forbidden Transitions
•
•
•
•
•
ΔL = 0, +/- 1
Δl = 1
ΔJ = 0, +/- 1, except that J=0 -> J=0 is forbidden.
ΔS = 0
ΔM = 0, +/- 1, except that M=0 -> M=0 is
forbidden if ΔJ=0.
• As the atoms become more complex, strict
L-S coupling fails and selection rules weaken
• http://physics.nist.gov/Pubs/AtSpec/node17.html
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Multiplets
• Transitions arising from a one term to another
term give rise to a multiplet.
• The multiplicity of a term is given by 2S+1.
S=0 is a singlet term; S=1/2 is a doublet term;
S=1 is a triplet term; S=3/2 is a quartet term ...
• Alkali metals (S=1/2) form doublets (Li, Na, K
...).
• Ions with 2 e- in outer shell (He I, Ca I, Mg I)
form singlets or triplets.
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Neutral Sodium Grotrian Diagram
• Outer e- n=3
• Energy
depends on l
• Δl rule applies
• Na D line
from 3p spin
difference
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Neutral Helium
Grotrian Diagram
• one e- in 1s state
• e- spin interactions
in multi e- cases:
L-S coupling
• total spin=0,1
1S singlet
3S triplet
• e- stuck in high E
level is metastable
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M Degeneracy Broken By
Magnetic Fields - Zeeman Effect
• Normal Zeeman effect operates in a singlet
state and results in three lines:
lines with ΔM = 0, the π components, are
unshifted, polarized parallel to the field;
lines with ΔM = +/- 1, the σ components, are
shifted by +/- 4.7 X 10-13g λ2B, where
g = Lande g factor, λ = wavelength, and
B = strength of the magnetic field in Gauss.
• g = 1 + (J(J+1) + S(S+1) - L(L+1))/2J(J+1)
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Hyperfine Structure
• Coupling between the magnetic moment of
electron and the nuclear magnetic moment
• Quantum number I = net nuclear spin
• Construct F=I+J, for J-I,J-I+1, ... J+I-1, J+I.
• 2S1/2 ground state of H has J=1/2, I=1/2
(because the spin of the proton is ½).
F=1 corresponds to parallel spins for p and eF=0 to anti-parallel spins (lower energy)
Energy difference: 1420 MHz or 21 cm.
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Typical Energies of Interaction
• Central potential (configurations)
4 eV
• Electrostatic interaction
(L-S coupling, terms)
0.4 eV
• Spin-orbit interaction (e- magnetic field
and e- magnetic moment; fine structure)
10-4 to 10-1 eV
• Hyperfine structure (nuclear spin, isotope)
10-7 to 10-4 eV
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Transition Probabilities
(Mihalas Section 4.2)
• Recall Einstein coefficients for b-b transitions
• Express actual cross section with oscillator
strength fij
e 2 
h ij 
tot   f ij  Bij  
 4 
m c 
• fij from QM calculation (based on volume
coincidence of wave functions of two states)
or laboratory measurements

• Tabulated with the statistical weight: log gf
• http://www.nist.gov/pml/data/atomspec.cfm
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Molecular Structure
(Robinson 2007; Tennyson 2005)
• Molecules exist in cool atmospheres
• Consider simple diatomic molecule where
differences create dipole moment: ex. CO
• Quantum numbers rule the rotation rates,
vibrational states, electronic states
• Interaction with light causes transitions
between states (similarly to atomic boundbound transitions)
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Rotational States: 2 axes
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Vibrational transition:
With Rotational Level Change +/-1
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Vibration-Rotation Transitions
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Molecular bands
• Transition between two electron energy levels
splits into series of vibrational transitions, each
of which splits into several rotation transitions.
• Result is molecular band in spectrum in which
large numbers of lines collect at the band head
at the short wavelength end
• http://www.nist.gov/pml/data/molspecdata.cfm
http://spec.jpl.nasa.gov/ftp/pub/catalog/catform.html
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