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There is no universal, cheap, easy way to do identify unknown materials. There are some easy methods that apply to some materials: if something is attracted to a magnet then it is ferromagnetic, and probably contains a substantial amount of iron, nickel, or cobalt. There are a few other rules of thumb, but the general problem is complex and is the reason ...

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Well, the fancy experimental way would be to use things like mass spectrometry or x-ray diffraction, or many other techniques. Doing it without those machines though... maybe chemistry would be your best bet. If you had a suspicion of what the material might be, you could use known chemical reactions to see what it does and doesn't react with, what it ...

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The ratio of masses is 7:1 in the compound but Nitrogen has 14 times the mass of Hydrogen as single atoms so there must be twice as many Hydrogen atoms as Nitrogen atoms i.e. the formula must be NH_2

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The dipole transition matrix elements $\mathbf{d}_m$ and $\mathbf{d}_n$ are complex-valued vectors which are relatively easy to define. Their "direction" is a mathematical convenience, and it is essentially given by the vector divided by its modulus, for an appropriate interpretation of the latter. Consider first the case of a single molecule, with a ...

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Your diagram of 2 H -> He is extremely misleading. First, He has Neutrons and can't be made from just 2 H. It need deuterium and tritium and it's a multi-step process involving first making deuterium via $\beta^{+}$ decay. Also, your question and diagram seem to imply that there is a formula describing the curve you show but there isn't. Your curve is ...

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Not really an answer, but rather some organized comments. First, you may become disappointed but the trully fundamental laws, as we know them today, are not written in terms of force laws. Even though the concept of force is still present in Physics, it is not used in the way it was before and which seems to be the way you are thinking about them. Force is ...

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What laws (formulas) govern the fundamental forces of nature? None. Columb's law and Newton's law of gravitation classical explanations of electrostatics and gravitation,respectively. But the are no analogus formulas for fundamental interactions. They must be described in the context of Quantum field theory. QFT is to complex to give you a ...

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