Calculating hydrogen intensity lines how? tia sal22
Rick T
I'm trying to calculate hydrogen intensity lines but not sure how?
I can calculate the wavelength and frequency for hydrogen between
levels
Example:
n3 to n2 Wavelength is 6.56e-7 and Frequency is 4.56e16 -Balmer
series
n5 to n3 Wavelength is 1.281e-6 and Frequency is 2.339e16 -Paschen
series
n8 to n5 Wavelength is 3.738e-6 and Frequency is 8.019e15 -Pfund
series
I used the Rydberg Formula to find Wavelength:
http://en.wikipedia.org/wiki/Rydberg_formula
And I used this formula for Frequency:
frequency=Speed of light/ wavelength
Does anyone now where I can find an example of how to calculate the
line intensity?
It doesn't have to be exact just trying to do some verification. If
the
values calculated match ratio wise with the numbers measured between
the different levels. just looking
for a ball park figure
tia sal22
tadchem
The energy intensity of a single photon is h*nu.
The intensity of a spectral emission line depends on how many photons
are contributing to that line.
How many photons are you looking at?
Tom Davidson
Richmond, VA
Uncle Al
Google
hydrogen "oscillator strength" 67,800 hits
hydrogen "transition probability" 58,500 hits
"The hydrogen atom: precision physics of simple atomic systems," SG
Karshenboim, 2001
<http://134.147.148.178/ispcdocs/ispc11/content/11/11-0234.pdf>
nasty
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
tadchem
The intensity is, in energy per photon, h*nu, where nu is the
frequency of the specific photon.
How many photons are you worried about? If you can tell my how many
photons you are looking at, then you can calculate the intensity.
Tom Davidson
Richmond, VA
I.N. Galidakis
> Greetings
> I'm trying to calculate hydrogen intensity lines but not sure how?
[snip]
> It doesn't have to be exact just trying to do some verification. If
> the
> values calculated match ratio wise with the numbers measured between
> the different levels. just looking
> for a ball park figure
I don't think you can without a calibrated spectrograph. The intensity of the
lines will change depending on discharge current density, pressure, exact gas
composition and other unforseeable factors, such as thermal and/or pressure
broadening.
In fact it's much better to pick up the intensities from standardized NIST
tables, like this one:
http://physics.nist.gov/PhysRefData/ASD/lines_form.html
Fill in as follows:
H I
400 - 700 nm
Only with observed wavelengths
Units eV
> tia sal22
--
Ioannis
franklinhu
What you are running up against is one of the great FAILURES of
quantum mechanics since no one seems to be able to calculate the
intensities with any accuracy as far as I know.
[[Mod. note -- On the contrary, what the original poster is running up
against is the calculation of atomic spectra, which is one of the great
SUCCESSES of quantum mechanics... However, these calculations are quite
complicated (and the results depend on the pressure, temperature, and
other thermodynamic properties of the Hydrogen), and it appears that
the original poster probably doesn't have the physics background
needed to do the necessary calculations.
Actually implementing such calculations is a big job (PhD-thesis
sized or larger), and takes large-scale computer calculations as well.
Previous posters in this thread have already suggested some useful
references (assuming fluency in quantum mechanics, spectroscopy, and
maybe radiative transfer as well). Another possibility would be
a textbook in atomic spectroscopy. I have seen the book
'Spectrophysics' by Anne P Thorne (Chapman and Hall Ltd) recommended,
but have no personal knowledge of it myself. Another starting point
might be the Journal of Quantitative Spectroscopy & Radiative Transfer,
which publishes research papers on this topic:
http://www.elsevier.com/wps/find/journaldescription.cws_home/272/description
Astrophysicists (who do a lot of these calculations for stellar spectra)
call the result a "synthetic spectrum". So, one way to find lots of
references to such calculations is to go to
http://adsabs.harvard.edu/abstract_service.html
enter "synthetic spectra" into the "title words" field, select "AND"
for how to combine the words, then click "Send query". This returns
several hundred references. For example,
http://adsabs.harvard.edu/abs/2007CoSka..37..189N
http://adsabs.harvard.edu/abs/2005A%26A...443..735C
http://adsabs.harvard.edu/abs/2004cosp...35.2335F
all look quite relevant.
-- jt]]
Thomas
Hi Rick,
It depends on whether you consider the lines in absorption or
emission. In absorption, the line strength is proportional to the
resonant scattering cross section, which in turn is proportional to
the square of the quantum mechanical overlap integral of the two
states involved. If you can't calculate the latter explicitly, you can
use the fact that the absorption line strength is proportional to the
atomic decay probability A_i,k from the upper level k divided by the
cube of the frequency for the transition between two levels i..e. LS
~ A_i,k / nu^3 .
You can get the exact A_i,k values from tables like published at
http://physics.nist.gov/PhysRefData/ASD/lines_form.html . For large
principal quantum numbers you can use the formula A_m,n= 1.3*10^9
*m^-1.8 *(n-1)^-3.2 [1/sec] (m,n >>1) (see my website
http://www.plasmaphysics.org.uk/#atdecay for more).
In emission, the line strength is proportional to A_i,k times the
population density for the upper level k. In local thermodynamic
equilibrium, the latter is given by the Boltzmann distribution
(n_k n_1 *exp(-(E_k-E_1)/kT) where E_k is the energy of level k (in kT,
k is the Boltzmann constant though). This however would only be
applicable for very high particle densities. In general, one has to
calculate the population densities consistently for all levels of the
atom, which involves the solution of a couples systems of equations (see
my page http://www.plasmaphysics.org.uk/papers/radscat2.htm for more).
Thomas
Albert van der Horst
In article <4f09b84c-d7ed-44c2...@g22g2000prf.googlegroups.com>,
Suppose we have three states A B and C.
We want to compare A->B and A->C.
The intensity of the lines is proportional to the chance
of the transitions. As long as transitions are not prohibited
(if for example spin is not conserved) this chance can be
calculated.
This calculation goes like this:
With A B and C there is a space distribution of the electron
associated.
The greater the overlap between A and B the greater the chance
that the transition occurs. It is clear that those calculations
can predict the relative intensity between A->B and A->C transitions,
even if they don't give an absolute value,
This can be calculated with fair precision.
Even if this matter is glossed over in an elementary quantum
mechanics text book, on close reading you will find this
explanation and a reference to more specific material.
The actual calculations are technical and tedious.
>tia sal22
P.S.
Ignore other posters who try to explain that the intensity of the line
is proportional to how may atoms you have, and then complain that you
didn't tell them that number.
--
--
Albert van der Horst, UTRECHT,THE NETHERLANDS
Economic growth -- being exponential -- ultimately falters.
albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst
Thomas Smid
> principal quantum numbers you can use the formula A_m,n= 1.3*10^9
>
> In emission, the line strength is proportional to A_i,k times the
> population density for the upper level k. In local thermodynamic
> equilibrium, the latter is given by the Boltzmann distribution
> (n_k n_1 *exp(-(E_k-E_1)/kT) where E_k is the energy of level k (in kT,
> k is the Boltzmann constant though). This however would only be
> applicable for very high particle densities. In general, one has to
> calculate the population densities consistently for all levels of the
> atom, which involves the solution of a couples systems of equations (see
> my pagehttp://www.plasmaphysics.org.uk/papers/radscat2.htmfor more).
>
> Thomas
Just a correction/clarification here:
when I said "In absorption, the line strength is proportional to the
resonant scattering cross section, which in turn is proportional to
the square of the quantum mechanical overlap integral of the two
states involved", then this implied that the lower level is identical
for the lines considered. If different lower states are involved, one
needs to know (like for the emission line strength) the population
density of these levels, which in general can only be obtained by
solving a corresponding system of equations for all levels.
Thomas
franklinhu
>
> Astrophysicists (who do a lot of these calculations for stellar spectra)
> call the result a "synthetic spectrum". �So, one way to find lots of
> references to such calculations is to go to
> �http://adsabs.harvard.edu/abstract_service.html
> enter "synthetic spectra" into the "title words" field, select "AND"
> for how to combine the words, then click "Send query". �This returns
> several hundred references. �For example,
> �http://adsabs.harvard.edu/abs/2007CoSka..37..189N
> �http://adsabs.harvard.edu/abs/2005A%26A...443..735C
> �http://adsabs.harvard.edu/abs/2004cosp...35.2335F
> all look quite relevant.
>
> - Show quoted text -
The OP is clearly NOT requesting the calculation of atomic spectra.
The OP is quite clearly knowlegeable about calcualting the spectra for
hydrogen and is explicitly requesting "line intensity". Notice the OP
is only asking about hydrogen.
The original OP said:
"I used the Rydberg Formula to find Wavelength:
http://en.wikipedia.org/wiki/Rydberg_formula
And I used this formula for Frequency:
frequency=Speed of light/ wavelength
Does anyone now where I can find an example of how to calculate the
line intensity? "
The moderator has attempted to deflect this question by assuming it is
about line location, not intensity. I'd still be curious if anyone has
been able to calculate the line intensities for hydrogen.
As for calculating the atomic spectra for anything other than
hydrogen, it does indeed take a supercomputer to calculate these as it
appears to be a big curve fitting exercise. I am not that familiar
with these calculations, but inability to easily calculate the spectra
of even helium would seem to be another problem with QM. Show me a
calculation for the atomic spectra for Helium based on QM. I'd like to
see that.
I would continue to assert that the inability to calculate line
intensities is a failure of QM.
[ Mod. note: It would be, if the said inability were true. Fortunately,
it is not. The literature on line intensities and multi-electron
atomic spectra is old and vast, with earliest work going back to the
1920s and '30s. The answers to both your challenges can be found in the
classic (though far from modern) reference
Bethe & Salpeter, _Quantum Mechanics of One- and Two-Electron
Atoms_, (Springer, 1957).
The situation has only improved since. -ik ]