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Natural Science Forum / Physics / Research / September 2008Exact value of Hydrogen line?
A few simple questions: 1) Whats the exact value of Hydrogen line? 2) And under what condition(s) is this value holds true? Regards, Jay Bala. > A few simple questions: > > 1) Whats the exact value of Hydrogen line? > 2) And under what condition(s) is this value holds true? There are lots of them. See eg http://en.wikipedia.org/wiki/Hydrogen_spectral_series If you mean the H-alpha line, it is given to 6 sig. fig. at http://en.wikipedia.org/wiki/H-alpha Exact value would be what you would expect to see if emitter and detector are in the same state of motion at essentially the same location. > A few simple questions: > [quoted text clipped - 3 lines] > Regards, > Jay Bala. At rest with respect to the observer in vacuum. Which hydrogen line? The "21 cm" hyperfine transition is 1.4204057517667 GHz. The H-alpha transition is 656.281 nm. There are lots more. http://en.wikipedia.org/wiki/Hydrogen_spectral_series http://en.wikipedia.org/wiki/Lyman_series etc. The Lyman transition is 121.6 nm - and it's a doublet, n = 2 orbital, j = 1/2 and j = 3/2.  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 Lets take the hyperfine, appears to be a basic and simpler model, c/f= gives just a little over 21 cm right? Also, what is the measurement error of this frequency? Considering the time (seconds) and length (meters) are man made numbers, is there some measurements or ratios that expresses these values where these units cancel? Regards, Jay Bala. > The "21 cm" hyperfine transition is 1.4204057517667 GHz. > Lets take the hyperfine, appears to be a basic and simpler model, > [quoted text clipped - 10 lines] > >> The "21 cm" hyperfine transition is 1.4204057517667 GHz. The "natural width" is determined by Heisenberg Uncertainty delta E delta t => h/(4pi) delta (h*f/2) * delta t => h/(4pi) delta (f) * delta t => 1/(2pi) delta t is the life time of the excited state delta E is energy of transition which is extremely long in case of the 21 cm line as observed in the astrophysical context making its "natural width" very small as Uncle Al's number would imply. Richard D. Saam > > Lets take the hyperfine, appears to be a basic and simpler model, > [quoted text clipped - 21 lines] > delta t is the life time of the excited state > delta E is energy of transition This doesn't sound right. Delta t relates to the length of the wave train, hence the duration of the transition, not the lifetime of the excited state, before it relaxes. Delta E relates to the spread of frequencies in the wave train, not to the energy of the transition (which determines the centre frequency) It is probably also worth mentioning that this "tight" uncertainty constraint of h/(4pi) applies when the uncertainty is defined as the standard deviation (sigma) for each component. Hence a more conservatively meaningful interpretation of the duration of the wave train would be 2 sigma....wouldn't it? You would then have nearly a 70% (fighting) chance of finding it somewhere in the range where you think it is. >>> Lets take the hyperfine, appears to be a basic and simpler model, >>> c/f= gives just a little over 21 cm right? [quoted text clipped - 24 lines] > Delta E relates to the spread of frequencies in the wave train, not to > the energy of the transition (which determines the centre frequency) In terms of the 21 cm hydrogen line, http://en.wikipedia.org/wiki/Hydrogen_line#Cause_of_the_hydrogen_line "This transition is highly forbidden with an extremely small probability of 2.9E−15 /sec. This means that the time for a single isolated atom of neutral hydrogen to undergo this transition is 1/2.9E−15 or 3.4E14 seconds" from above: delta f * delta t => 1/(2pi) delta f * 3.4E14 => 1/(2pi) delta f => 4.68E-16 Hz The above observed significant digit frequency 1.4204057517667 GHz = 1,420,405,751.7667 Hz Apparently other effects (doppler ) are broadening the width beyond the natural lifetime Heisenberg uncertainty line width. Richard D. Saam > >>> Lets take the hyperfine, appears to be a basic and simpler model, > >>> c/f= gives just a little over 21 cm right? [quoted text clipped - 48 lines] > are broadening the width beyond the > natural lifetime Heisenberg uncertainty line width. The observed error margin is ~ 5 E-5 The theoretical error margin is ~ 5 E-16 Just as the theoretical error margin requires an emission time of ~ 10 million years, the same applies for the required detection time. The difference between the 2 error margins is ~ E 11 corresponding to a required detection time of ~ 1 hour. This sounds reasonable. > The observed error margin is ~ 5 E-5 > The theoretical error margin is ~ 5 E-16 [quoted text clipped - 3 lines] > difference between the 2 error margins is ~ E 11 corresponding to a > required detection time of ~ 1 hour. This sounds reasonable. It would be interesting to know if the observational error margin ~ 5 E-5 Hz in the observed frequency of astrophysical hydrogen 21 cm 1.4204057517667 GHz = 1,420,405,751.7667 Hz represents a limit below which astrophysical electromagnetic frequencies cannot be observed. Are any electromagnetic waves observed below 5 E-5 Hz ? Richard D. Saam You mean observed or measured? Regards, Jay Bala. > It would be interesting to know > if the observational error margin ~ 5 E-5 Hz [quoted text clipped - 3 lines] > below which astrophysical electromagnetic frequencies > cannot be observed. > > The observed error margin is ~ 5 E-5 > > The theoretical error margin is ~ 5 E-16 [quoted text clipped - 13 lines] > > Are any electromagnetic waves observed below 5 E-5 Hz ? In principle, yes, but we are now straying into areas of practical eletronics. If it were possible to produce a sufficiently high Q tuned filter to admit a still tighter pass band, then that would pick out which ever frequency it was tuned to. However, you would still end up with the pulse from fthe filter being ten times as long if the spread was reduced by a factor of ten. >>> The observed error margin is ~ 5 E-5 >>> The theoretical error margin is ~ 5 E-16 [quoted text clipped - 18 lines] > with the pulse from fthe filter being ten times as long if the spread > was reduced by a factor of ten. Yes "in principle" but such a long period 1/ 5 E-5 Hz = 20,000 seconds (333 minutes) (5.6 hours) may be an extreme test of practical electronic instrumentation, but given such practical electronic instrumentation: Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ? Richard D. Saam > >>> The observed error margin is ~ 5 E-5 > >>> The theoretical error margin is ~ 5 E-16 [quoted text clipped - 28 lines] > > Richard D. Saam The point is that ALL frequencies within this range exist, via Fourier analysis. A 5.6 hour aperture for an astrophysical source would introduce serious Doppler shifts due to the Earth's rotation. This would broaden not narrow the spectrum (unless you, personally, are prepared to finance a radio observatory at the South Pole) >>>>> The observed error margin is ~ 5 E-5 >>>>> The theoretical error margin is ~ 5 E-16 [quoted text clipped - 32 lines] > not narrow the spectrum (unless you, personally, are prepared to > finance a radio observatory at the South Pole) Which brings up the point: From where was the frequency range observed (including the +/- 5 E-5 Hz)? 1.4204057517667 GHz = 1,420,405,751.7667 Hz The fundamental question is: What broadens the Heisenberg Uncertainty 5E-16 Hz to 5E-5 Hz? > >>>>> The observed error margin is ~ 5 E-5 > >>>>> The theoretical error margin is ~ 5 E-16 [quoted text clipped - 40 lines] > The fundamental question is: > What broadens the Heisenberg Uncertainty 5E-16 Hz to 5E-5 Hz?- Hide quoted text - I have already answered that. The limited time available to make the observation. > >>>>> The observed error margin is ~ 5 E-5 > >>>>> The theoretical error margin is ~ 5 E-16 [quoted text clipped - 37 lines] > (including the +/- 5 E-5 Hz)? > 1.4204057517667 GHz = 1,420,405,751.7667 Hz Given that hydrogen is the simplest thing to model theoretically, I would not be too surprised if it turns out to have been derived from theory. > The fundamental question is: > What broadens the Heisenberg Uncertainty 5E-16 Hz to 5E-5 Hz Under that theoretical scenario, that would be the limit of accuracy of the theoretical model. Richard Saam skrev: > Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ? The typical plasma frequency of the interstellar medium is on the order of some kHz, which means that electromagnetic waves of lower frequency will be rapidly damped out. Of course, any observatory that we build will at least be located inside the solar wind, and usually even inside the Earth's ionosphere, where the plasma frequency is even higher (MHz in case of the ionosphere), which sets the lower limit on the frequency of astrophysical electromagnetic waves that we can observe. Ulf Torkelsson > Richard Saam skrev: >> Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ? [quoted text clipped - 9 lines] > > Ulf Torkelsson Yes, there are these plasma frequencies as you describe but: What is the 'rapidly damped out' time of other incident frequencies and can this dampening be used as an observational tool? Assuming there is some type of ~1E-5 hz astrophysical generator (dark matter and/or energy as in post 'hypothesis for dark matter'), do we see these plasma frequency damping out effects on a complementary frequency order of 1E-5 hz (or harmonics thereof) in accordance with the following observations: ***D. Saul Davis, Paul Hickson, Glen Herriot, Chiao- Yao She Temporal variability of the telluric sodium layer Science 24 http://arxiv.org/abs/astro-ph/0609307 ***K. Pounds , R. Edelson, A. Markowitz, S. Vaughan X-ray Power Density Spectrum of the Narrow Line Seyfert1 Galaxy Akn 564, http://arxiv.org/abs/astro-ph/0101542 ***Kotov V.A., Lyuty V. M., Haneychuk V. I. : "New evidences of the 160-minute oscillations in active galactic nuclei", 1993, Izv. Krym. Astrofiz. Obs., Tom 88, p. 47-59. ***Interstellar scintillation of AGN http://www.jive.nl/science/iss.html ***Kiwamu Nishida, Naoki Kobayashi, Yoshio Fukao Resonant Oscillations Between the Solid Earth and the Atmosphere Science 24 March 2000 Vol. 287. no. 5461, pp. 2244 – 2246 and perhaps these damping effects result in tidal forces of a magnitude to affect planetary flybys: ***John D. Anderson, James K. Campbell, Michael Martin Nieto, The energy transfer process in planetary flybys http://arxiv.org/abs/astro-ph/0608087 and cause the anomalous Gravity Probe B Polhode motions of superconductor supercurrents: ***Gravity Probe B Gyro #1 Polhode Motion Animations http://einstein.stanford.edu/Media/Polhode_motion-animation.html Richard D. Saam Richard Saam skrev: >> Richard Saam skrev: >>> Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ? [quoted text clipped - 13 lines] > What is the 'rapidly damped out' time of other incident frequencies > and can this dampening be used as an observational tool? The electromagnetic waves become evanescent below the plasma frequency and are damped out within at most a few wavelengths or periods if you prefer to think in terms of the time scale. For that reason there is no way of observing these waves from an astrophysical source. Having said this though one should keep in mind that there are other forms of waves that can propagate through a plasma at a frequency below the plasma frequency, for instance Alfven waves. Such waves can be measured in situ in the magnetosphere and the solar wind. One should also keep in mind that although one cannot have an electromagnetic wave at a frequency below the plasma frequency it is possible to observe slow modulations in waves with higher frequencies, which is the way a radio works. > Assuming there is some type of ~1E-5 hz astrophysical generator > (dark matter and/or energy as in post 'hypothesis for dark matter'), > do we see these plasma frequency damping out effects > on a complementary frequency order of 1E-5 hz (or harmonics thereof) > in accordance with the following observations: Assuming some new physics you can always explain any observation that you want to explain, but most of the time the same phenomenon can also be explained by more mundane mechanisms that are based on established physics. As far as I can tell essentially all of the observations that you list can be explained in the latter way, and sometimes it is even possible to find more than one explanation based on conventional physics, because there is insufficient data. > ***D. Saul Davis, Paul Hickson, Glen Herriot, Chiao- Yao She Temporal > variability of the telluric sodium layer Science 24 [quoted text clipped - 28 lines] > ***Gravity Probe B Gyro #1 Polhode Motion Animations > http://einstein.stanford.edu/Media/Polhode_motion-animation.html The last two examples illustrate another problem. These are small effects in highly complex experiments, which are also influenced by the environment in a number of different ways, which might not even be completely understood by the experimentalists themselves, since they only have a limited knowledge of and control of the environment surrounding their instruments. Ulf Torkelsson > Richard Saam skrev: >>> Richard Saam skrev: [quoted text clipped - 83 lines] > > Ulf Torkelsson On the subject of Alfen_wave: http://en.wikipedia.org/wiki/Alfven_wave "The ion mass density (ni mi) provides the inertia and the magnetic field (B) line tension provides the restoring force." such that: v = B / sqrt(4 pi ni mi) v = velocity B = magnetic field ni = ion number concentration mi = ion mass mu = magnetic permeability then: mi v^2 ~ B^2 volume / (4 pi) To which Enrico Fermi in 1949 nodded his head exclaiming "of course". Eugene Parker "Conversations on Electric and Magnetic Fields in the Cosmos (Princeton Series in Astrophysics)" does not say 'of course' could be applied to an analogous argument for an electric field (E) and its displacement (D) in that same 'volume' mi v^2 ~ D E volume / (4 pi) But if electric fields (E & D) as well as (H & B) were involved as restoring forces, all of the examples could be explained in terms of gravitational tidal effects related to a significant portion of the observable universe critical mass (~1E56 g) (dark energy dark matter?) oscillating in accordance with these restoring forces at ~1e-5 hz with a related van Alfen wave mechanism As an aside, Eugene Parker makes a strong case for the cgs system use in research analysis because dimensional units are the same for E,D,H & B (g ^ (1/2) cm ^ (-1/2) sec ^ -1) and can be compared on that basis, an attribute that does not exist in the SI system. Richard D. Saam > >>> Lets take the hyperfine, appears to be a basic and simpler model, > >>> c/f= gives just a little over 21 cm right? [quoted text clipped - 48 lines] > are broadening the width beyond the > natural lifetime Heisenberg uncertainty line width. These figures do seem to make a nonsense of the idea that del t in the uncertainty relationship also represents the time window needed to observe the radiation to that accuracy of resolution. Clearly we haven't had mirowave detectors on Earth for 10 million years, or even for the thousand years or more needed for the observed (lesser) resolution. I'm not sure how that point is resolved. C |
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