Saha*Boltzmann Problem
You got your Si I line and know the upper and lower level energies.
Now we want to figure out what fraction of all silicon N(Si) is in your lower level --ionization stage r, excitation s-- N(r,s) at some temperature and electron pressure --we want N(r,s)/N.
The assignment involves working out this fraction at
T=Your line wavelength in angstroms (Kelvin),
Pe=2.5 [dyne/cm2]. Yes, 2.5 is the value to use.
So the temprature used for a 4294.092 angstrom line would be 4294.092 K. Hey, λ is independent of T, this is a trick so each student will have a different temperature! (note that Q=5040/T)
I assume you have familiarised yourself with the Saha Boltzmann notes...
***Nomenclature****
N stands for total number density of atoms, in this case silicon.
Nr stands for the number density of atoms in the r-th stage of ionization,
Nr,s stands for the number density of atoms in the r-th stage of ionization and s-th stage of excitation.
Nr=sum of all Nr,s
N=sum of all Nr
You want Nr,s/N.
Note that astronomers use cgs units (still!) so the Saha factor is
Nr/N = Nr/(Nr-1+Nr+Nr+1) = 1/(Nr-1/Nr+1+1+Nr+1/Nr)
where
Nr+1/Nr = (Ur+1/Ur)*(109.08-Q Ir)/Q5/2Pe
The partition functions and ionization potentials for silicon are
Silicon atomic data:
The IP are 8.149, 16.340, and 33.460 eV.
Partition functions (Allen, Astrophysical Quantities)
T U(1) U(2) U(3) U(4)
coming soon....
Si partition function polynomial fits, T=temperature/1000 (Use these!)
C S I L I C O N
U1 = 6.08+(.811-.031*T)*T
U2 = 2.+4.*EXP(-.414/T)
U3 = 2.+12.*EXP(-33.01/T)
SAHA BOLTZMANN worksheet
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Saha factor N(r)/N=N(2)/N:
My wavelength w=
Temperature T=
Theta=5040/T=
T/1000=
Partition functions (remember to use T/1000)
U1=
U2=
U3=
Saha ratios
N2/N1=
N3/N2=
N(1)/N=
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Boltzmann factor
g(r,s)=g(1,ep)=
U(r,s)=U(1,T) =
lower ep (eV) =
theta=
N(1,ep)/N(1)=
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Answer
N(1,ep)/N(1) * N(1)/N =
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