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Unformatted text preview: (VII.25) D
L ln 2
D,0 D ij ln 2
c 8kT
m ij !"#$%$ Molecular Spectra 3
Copyright © 2009 by Jerry M. Seitzman. All rights reserved. What we may need to know for the exam:
How does the Doppler broadening scale? scaling like cbar (average velocity) and a freq.
How does the Collision broadening scale? scaling like collision frequency School of Aerospace Engineering Line Broadening (con’t)
• For isolated transitions of neutral molecules,
If lines overlap significantly, can
these are dominant effects
get line “narrowing” effects
– all occur simultaneously
u du
• Voigt Profile
Vv
Du
D
– convolution of indep. broadening effects
V v a
ij 2 ln 2 D a ln 2 e D,0 L
D Molecular Spectra 4
Copyright © 2009 by Jerry M. Seitzman. All rights reserved. y y2 dy
2
ya 1 (VII.26) u ln 2
D2 a<< 1
a>>1 Doppler
Lorentz (Collision) D
L ij !"#$%$ 2 Ex. at 5 microns @ 2400 K
what dominates?
School of Aerospace Engineering at 10 atm, collision broad
at 0.1 atm, 2400 K,
Doppler like 3*bigger than
Collision
at 500 nm, 300 K, in
b etween the two
p ressures.
a t 500 nm, high T, and P,
they are comprable again
Different broadenings
b ecome important in
d ifferent conditions Doppler vs. Collision Broadening
• Typical values
– collision broadening
• 0.10.2 cm1 at 1 atm, 300 K
p
c c , STP n T
TSTP pSTP (cm1) Shows the pressure
inﬂuence. Facter of 10
change in pressure, Factor
0.1 atm 10 atm o f 10 change in broad. 300 K 0.01 1.0 2400 K , n ~ 0.5 0.0035 0.35 Factor 8 change in T,
factor 3 change in broad – Doppler broadening
D 7.1623 10 7
ij N2, (cm1) 500 nm TK
MW 300 K • Doppler tends to “dominate”
at low p, high T, short Doppler Broad is small for
longer wavelengths 5m 0.047 0.0047 2400 K 0.13 0.013 !"#$%$ Molecular Spectra 5
Copyright © 2009 by Jerry M. Seitzman. All rights reserved. A t high T (2400 K) there is
a h uge difference for
shoreter wavelengths.
A t 5 microns, same huge
d ifference but numbers are
very small
Wave number where
we get the most
a bsorption School of Aerospace Engineering • So far considered
single transitions
• But will normally
have many radiative
transi...
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 Summer '08
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