Spectroscopy is so cool :) One question about it: Is it possible to construct two samples made of different elements which have an indistinguishable spectrum? Or are the spectral 'fingerprints' of each element sufficiently unique?
Sounds like a problem that one could formalize in linear algebra, maybe ... if we treat each wavelength as a dimension in a real-valued vector space and each spectral fingerprint as a vector, the question is whether the set of all these vectors is linearly independent, I think.
That's a very interesting question. I think that the spectrum contains all of the information about the possible energies of electrons in the atoms or molecules in question, which I think is the same information that determines how the element or compound reacts chemically (since chemistry is all about the motion of electrons). So I think that two compounds with truly indistinguishable spectra would also be chemically indistinguishable, which seems highly unlikely.
Mathematically, I think that the relevant point is that the set of possible compounds is discrete - because they are combinations of whole numbers of atoms from a finite set of elements - while the set of possible wavelengths is continuous, so the set of actually realised spectra is a measure zero subset of the space of possible spectra. I think that this means that, unless there were some intrinsic symmetry which allowed you to construct matching molecules in a particular way (which I don't think there is), then the probability of two molecules having the same spectrum will be zero.
Another article explaining stuff so well! I assume there is some limit to spectroscopy’s ability to detect a multiple number of different elements in that once you get above a certain complexity of elements there would be overlaps (like overpaying multiple QR codes) in the spectroscopic image and thus some degree of ambiguity could set in. Or maybe this is resolved through obtaining finer and finer images
That's a great question! Absolutely, the more complex a spectrum becomes, the more difficult it is to precisely determine the exact composition. Fortunately, there are only 92 naturally occurring elements so there is not too much capacity for overlap, and the spectral lines they produce can be resolved very finely. The context in which spectroscopy becomes much more challenging is when there are complex molecules consisting of many different atoms bound together, since there are in principle an infinite number of possible molecules and the spectra they each produce can be very messy. However, in stars this is not an issue since the temperatures are too high for different atoms to bond together to form compounds, which is an important part of why spectroscopy is so effective for studying stars.
Thanks again Paul, two last questions on this. H2O is a relatively simple molecule does it have a distinct spectroscopy that can be distinguished from hydrogen and oxygen on their own? Secondly can we see the spectroscopy of any detected planets (outside our solar system) or it the “signal” too small
1) Absolutely! The chemical bonding between atoms in molecules actually leads to spectra that look quite different from those of the individual atoms. There are characteristic features specifically of a hydrogen atom bonded to an oxygen atom that can be seen with spectroscopy which can allow you to identify water. These particular features are observed in infrared light that is invisible to the naked eye, but with the right equipment they can be analysed just the same way as the visible light of stars. The challenge is that lots of more complex molecules also contain oxygen and hydrogen atoms bonded together and will show the same features, but water can still be identified by the lack of other features that those molecules would show.
2) Absolutely, this is one of the plans for the recently launched James Webb Space Telescope. There's a short video from NASA talking about it here: https://youtu.be/jbSXBbyWsTE. As far as I know there are not results from this yet, though.
Spectroscopy is so cool :) One question about it: Is it possible to construct two samples made of different elements which have an indistinguishable spectrum? Or are the spectral 'fingerprints' of each element sufficiently unique?
Sounds like a problem that one could formalize in linear algebra, maybe ... if we treat each wavelength as a dimension in a real-valued vector space and each spectral fingerprint as a vector, the question is whether the set of all these vectors is linearly independent, I think.
That's a very interesting question. I think that the spectrum contains all of the information about the possible energies of electrons in the atoms or molecules in question, which I think is the same information that determines how the element or compound reacts chemically (since chemistry is all about the motion of electrons). So I think that two compounds with truly indistinguishable spectra would also be chemically indistinguishable, which seems highly unlikely.
Mathematically, I think that the relevant point is that the set of possible compounds is discrete - because they are combinations of whole numbers of atoms from a finite set of elements - while the set of possible wavelengths is continuous, so the set of actually realised spectra is a measure zero subset of the space of possible spectra. I think that this means that, unless there were some intrinsic symmetry which allowed you to construct matching molecules in a particular way (which I don't think there is), then the probability of two molecules having the same spectrum will be zero.
Another article explaining stuff so well! I assume there is some limit to spectroscopy’s ability to detect a multiple number of different elements in that once you get above a certain complexity of elements there would be overlaps (like overpaying multiple QR codes) in the spectroscopic image and thus some degree of ambiguity could set in. Or maybe this is resolved through obtaining finer and finer images
That's a great question! Absolutely, the more complex a spectrum becomes, the more difficult it is to precisely determine the exact composition. Fortunately, there are only 92 naturally occurring elements so there is not too much capacity for overlap, and the spectral lines they produce can be resolved very finely. The context in which spectroscopy becomes much more challenging is when there are complex molecules consisting of many different atoms bound together, since there are in principle an infinite number of possible molecules and the spectra they each produce can be very messy. However, in stars this is not an issue since the temperatures are too high for different atoms to bond together to form compounds, which is an important part of why spectroscopy is so effective for studying stars.
Thanks again Paul, two last questions on this. H2O is a relatively simple molecule does it have a distinct spectroscopy that can be distinguished from hydrogen and oxygen on their own? Secondly can we see the spectroscopy of any detected planets (outside our solar system) or it the “signal” too small
1) Absolutely! The chemical bonding between atoms in molecules actually leads to spectra that look quite different from those of the individual atoms. There are characteristic features specifically of a hydrogen atom bonded to an oxygen atom that can be seen with spectroscopy which can allow you to identify water. These particular features are observed in infrared light that is invisible to the naked eye, but with the right equipment they can be analysed just the same way as the visible light of stars. The challenge is that lots of more complex molecules also contain oxygen and hydrogen atoms bonded together and will show the same features, but water can still be identified by the lack of other features that those molecules would show.
2) Absolutely, this is one of the plans for the recently launched James Webb Space Telescope. There's a short video from NASA talking about it here: https://youtu.be/jbSXBbyWsTE. As far as I know there are not results from this yet, though.