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Spectroscopy

Spectroscopy. 1990 Bruce Gold Medal 1937 AJC Prize. Spectral lines The Fraunhofer spectrum Charlotte Moore Sitterly (Allen!) Multiplet table Rowland table Formalism of spectroscopy. Quantum Numbers of Atomic States. Principal quantum number n defines the energy level

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Spectroscopy

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  1. Spectroscopy 1990 Bruce Gold Medal 1937 AJC Prize • Spectral lines • The Fraunhofer spectrum • Charlotte Moore Sitterly (Allen!) • Multiplet table • Rowland table • Formalism of spectroscopy

  2. Quantum Numbers of Atomic States • Principal quantum number n defines the energy level • Azimuthal quantum number l • states with l=0 called s states • states with l=1 called p states • states with l=2 called d states • states with l=3 called f states • “orbits” of s states become more eccentric as n increases • Electron transitions take place between adjacent angular momentum states (i.e. Dl=1) • “sharp series” lines from p to higher s states • “principal series” lines from s to higher p states • “diffuse series” lines from p to higher d states • “fundamental series” lines from d to higher f states • The first line(s) of the principal series (s to p) are called resonance lines since it involves the ground level • In alkali metals, the p, d, and f energy levels are doubled (e.g. the Na D lines) due to the coupling between the magnetic moment of the orbital motion and the spin of the electron (the quantum number s, which can be +1/2 or –1/2

  3. Spectroscopic Notation • The total angular momentum quantum number is j = l +S* • For s states, j=1/2 • For p states, j=1/2 or j=3/2 • Electron levels are designated by the notation “n2(L)J” • n is the total quantum number • The superscript 2 indicates the levels are doubled • L is the azimuthal quantum number (S,P,D,F) • J denotes the angular momentum quantum number • For the sodium ground level is 3s2S1/2 • The two lowest p levels are 3p2P1/2 and 3p2P 3/2 • The Na D lines are described • 3s2S½ - 3p2P3/2 l5889.953 and 3s2S½ - 3p2P1/2l5895.923 * This is a different S than the s state!

  4. More Spectroscopic Vocabulary • The Pauli exclusion principle requires that two s-electrons in the same state must have opposite spin • Therefore S=0 and these are called “singlet” states • The ground state of He is a singlet state – 1S0 • The superscript 1 means singlet • The subscript 0 means J=0 • In the first excited state of He, one electron is in the 1s state, and the second can be in either the 2s or the 2p state. • Depending on how the electrons’ spins are aligned, these states can either be singlets or triplets • Electrons can only jump between singlet states or between triplet states

  5. It goes on and on and on… • The state of the electrons is described with a term for each electron above the closed shell. • For carbon atoms, “1s22s22p2”says there are • 2 electrons in the 1s state • 2 electrons in the 2s state • 2 electrons in the 2p state • Allowed and forbidden transitions • Transitions with Dl=1 and DJ=1 and 0 are allowed (except between J=0 and J=0) • Other transitions are forbidden • For some electron states there are no allowed transitions to lower energy states. Such levels are called metastable • The situation is more complex in atoms with more electrons • A multiplet is the whole group of transitions between two states, say 3P-3D

  6. Grotrian Diagram for He • Struve and Wurm 1938, ApJ

  7. Grotrian Diagram for Li I NIST

  8. Grotrian Diagram for O I NIST

  9. Fraunhofer Lines

  10. Spectral Line Formation • Classical picture of radiation • Intrinsic vs. extrinsic broadening mechanisms • Line absorption coefficient • Radiative transfer in spectral lines

  11. Spectral Line Formation-Line Absorption Coefficient • Radiation damping (atomic absorptions and emissions aren’t perfectly monochromatic – uncertainty principle) • Thermal broadening from random kinetic motion • Collisional broadening – perturbations from neighboring atoms/ions/electrons) • Hyperfine structure • Zeeman effect

  12. Classical Picture of Radiation • Photons are sinusoidal variations of electro-magnetic fields • When a photon passes by an electron in an atom, the changing fields cause the electron to oscillate • Treat the electron as a classical harmonic oscillator: mass x acceleration = external force – restoring force – dissipative • E&M is useful! (well…)

  13. Atomic Absorption Coefficient • N0 is the number of bound electrons per unit volume • the quantity n-n0 is the frequency separation from the nominal line center • the quantity e is the dielectric constant (e=1 in free space) • and g=g/m is the classical damping constant The atomic absorption coefficient includes atomic data (f, e, g) and the state of the gas (N0), and is a function of frequency. The equation expresses the natural broadening of a spectral line.

  14. The Classical Damping Constant • For a classical harmonic oscillator, • The shape of the spectral line depends on the size of the classical damping constant • For n-n0 >> g/4p, the line falls off as (n-n0)-2 • Accelerating electric charges radiate. • and • is the classical damping constant (l is in cm) The mean lifetime is also defined as T=1/g, where T=4.5l2

  15. The Classical Damping Line Profile

  16. The Classical Line Profile • Look at a thin atmospheric layer between t2 (the deeper layer) and t1 • The line profile is proportional to kn • At line center n=n0, and • Half the maximum depth occurs at (n-n0)=g/4p • In terms of wavelength • Very small – and the same for ALL lines!

  17. An example… • The Na D lines have a wavelength of 5.9x10-5 cm. g = 6.4 x 107 sec-1 • The absorption coefficient per gram of Na atoms at a distance of 2A from line center can be calculated: Dn0-n = 1.7 x 1011 sec-1 and N = 1/m = 2.6 x 1022 atoms gm-1 • Then k = 3.7 x 104f • and f=2/3, so k = 2.5 x 104 per gram of neutral sodium

  18. The Abundance of Sodium • In the Sun, the Na D lines are about 1% deep at a distance of 2A from line center • Use a simple one-layer model of depth x (the Schuster-Schwarzschild model) • Or krx=0.01, and rx=4x10-7 gm cm-2 (recall thatkNa=2.5 x 104 per gram of neutral sodium at a distance of 2A from line center) • the quantity rx is a column density

  19. Line Absorption with QM • Replace g with G! • Broadening depends on lifetime of level • Levels with long lifetimes are sharp • Levels with short lifetimes are fuzzy • QM damping constants for resonance lines may be close to the classical damping constant • QM damping constants for other Fraunhofer lines may be 5,10, or even 50 times bigger than the classical damping constant

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