Spectroscopy
description
Transcript of Spectroscopy
SpectroscopySpectroscopy
• Spectral lines• The Fraunhofer spectrum• Charlotte Moore Sitterly (Allen!)
– Multiplet table– Rowland table
• Formalism of spectroscopy
Quantum Numbers of Atomic Quantum Numbers of Atomic StatesStates
• 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. l=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
Spectroscopic NotationSpectroscopic 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 5889.953 and 3s2S½ - 3p2P1/2 5895.923
* This is a different S than the s state!
More Spectroscopic VocabularyMore 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
It goes on and on and on….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 Allowed and Forbidden TransitionsTransitions
• Transitions with l=1 and J=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
Grotrian Grotrian Diagram for Diagram for
HeHe
• Struve and Wurm 1938, ApJ
Spectral Line FormationSpectral Line Formation
• Classical picture of radiation• Intrinsic vs. extrinsic broadening
mechanisms• Line absorption coefficient• Radiative transfer in spectral lines
Spectral Line Formation-Line Spectral Line Formation-Line Absorption CoefficientAbsorption 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
Classical Picture of RadiationClassical 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!
Atomic Absorption CoefficientAtomic Absorption Coefficient
• N0 is the number of bound electrons per unit volume
• the quantity -0 is the frequency separation from the nominal line center
• the quantity e is the dielectric constant (=1 in free space)• and g/m is the classical damping constant
220
20
)4()(
4
mc
N
The atomic absorption coefficient includes atomic data (f, , ) and the state of the gas (N0), and is a function of frequency. The equation expresses the natural broadening of a spectral line.
The Classical Damping ConstantThe Classical Damping Constant
• For a classical harmonic oscillator,• The shape of the spectral line depends on the size of the
classical damping constant• For -0 >> /4, the line falls off as (-0)-2
• Accelerating electric charges radiate.
• and
• is the classical damping constant ( is in cm)
220
20
)4()(
4
mc
N
Wmcdt
dW3
222
3
8
teWW 0
123
222
sec2223.0
3
8
mc
The mean lifetime is also defined as T=1/, where T=4.52
Line Absorption with QMLine Absorption with QM
• Replace with !• 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
The The ClassicalClassical Line Profile Line Profile• Look at a thin atmospheric layer between 2 (the
deeper layer) and 1
• The line profile is proportional to
• At line center =0, and • Half the maximum depth occurs at (-0)=/4• In terms of wavelength
• Very small – and the same for ALL lines!
)1)(()()( 112 xIeII x
)()()( 112 xIII
mcN24
Amc
cc000118.0
3
2
4 2
2
2212
21
The Classical Damping Line ProfileThe Classical Damping Line Profile
An example…An example…
• The Na D lines have a wavelength of 5.9x10-5 cm. = 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:
0- = 1.7 x 1011 sec-1 andN = 1/ = 2.6 x 1022 atoms gm-1
• Then = 3.7 x 104 f• and f=2/3, so
= 2.5 x 104 per gram of neutral sodium
The Abundance of SodiumThe 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 x=0.01, and x=4x10-7 gm cm-2
99.00
xeI
I