How can i calculate electron number in element sub shell= spdf sistem by experiment without aofbau rules.?
The behavior of the Periodic Table is very important experimental evidence to the quantum behavior of electrons, because it was known 50 years before physicists hit on quantum theory, and there you have it, the Table is arranged in ways that reflect the filling of electronic orbitals.
You may want to take a tour of how this was arrived at, and I'll try to explain it to you without too much emphasis on the details of quantum theory, with which you may not be throughout familiarized.
So let's us try to drive in the road to THE AUFBAU RULES:
1) For sake of starting at the start, by the beginning of the XX century scientists knew that atoms had electrons inside, and very dense lumps of matter making up the nucleus. The odd thing was, that electrons in orbits around the nucleus should radiate away all their energy, so scientists did not know how electrons inside atoms could be stable in the first place.
2) Max Planck, and later Einstein were proposing very simple solutions to very complicated problems by simply assuming the energy and the energy in electromagnetic radiation (light, microwaves), comes in discrete packets they called quanta, and that we now call photons. Both knew, as did physicists at the time, that having light constituted by particles, and energy exchanged in discrete units would force a major new understanding in Physics, the theory of which was yet to be written.
3) On theoretical considerations alone the French physicist de Broglie wrote his PhD thesis proving that the light could behave like particles, then ordinary particles like the electron, and according to the Special theory of Relativity, would be able to behave like waves. This was an interesting beautiful syntheses, but also unusually bold in what Physics is concerned. Famously, it was Einstein intervention in support of these ideas, that got de Broglie his degree, with a thesis mysterious in nature and whose implications were not at all understood.
4) Confirmation of de Broglie's idea didn't take long (in relative terms). The Americans Davisson and Germer pursuing a completely different problem, were firing electrons at crystalline structures and getting wavelike results. By their experiments electrons did behave like waves.
5) But early quantum theory had already taken a different, also very bold, theoretical step. As mentioned, electrons should not be stable orbiting the nucleus, they should instead radiate their energy away and eventually fall into the nucleus. Niels Bohr, a Danish physicist, decided to take for granted what Nature was saying. If electrons do not fall to the nucleus, then they don't. They may have a select group of states, they may jump between them, and that's it. Why there are no intermediate states allowing the electron to "slide" and radiating energy, was not known.
6) Initially Bohr's ideas met considerable skepticism and was not considered a complete theory of the atom, not even by Bohr himself. Everybody knew something better would have to come along. But in its day, it did give correctly the value for a mysterious constant (Rydberg constant) and the frequency of radiation of electronic transitions for hydrogenoid ions. Rydberg on a completely empirical basis had worked a formula, with his constant, that was valid only in some transitions, while Bohr gave a framework allowing some understanding of where the constant came from, and making Rydberg's formula useful with many other transitions.
7) I have to double emphasize the importance of Bohr's theory. Though wrong from a fundamental point of view it did yield practical results quite striking. It was known that ions when excited would radiate energy at very specific frequencies and now Bohr's theory allowed to compute them and have some understanding of why they occurred. Dirac, years later, would say that the atom radiating specific frequencies and not a continuum, would be impossible to describe by any conceivable classical scheme of forces.
8) In case you're wondering, it's from those days that the labels s, p, d come from. They refer to how spectral lines would appear to the observer "s" being sharp, "d" diffuse, "p" I'm not sure...
9) Bohr's theory had been quite successful by some standards and scientists were working in refinements of it that would increase its accuracy. Meanwhile, de Broglie published his thesis arguing that matter would, in some circumstances, behave like a wave, which got everybody thinking. If the electron may have wavelike behavior where's the wave equation? In a stroke of genius Schrodinger published, without much thought of what it meant, a condition for a function, whose solutions allowed to compute the energy levels of atomic hydrogen. Because physicists do not like rabbits magically coming out of hats, eventually Schrodinger had to concede his intuition saying he was thinking the simplest wave equation one could have in one dimension to describe electrons in atoms. The specific meaning of the function used would only become apparent a few years later, when Max Born proposed it was a probability density amplitude.
10) For completeness to this train of events, I have to mention that before Schrodinger, Heisenberg had been working on a different mathematical approach to the problem but it was shown to be equivalent to Shrodinger's wave-functions. And that Schrodinger's equation is not relativistic, that is, it's not written in a way that complies with the Theory of Relativity. The honor of that achievement, the wave equation for electrons fully consistent with Relativity, would befall on Paul Dirac.
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You may already imagine where this is going. To describe a quantum system we use a wave equation (Shrodinger's or Dirac's) and we try to get the solutions, the wave-functions whose properties describe the system.
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I did not log in for a few days and only now did I see your email. I was getting into a long winded answer about how you get the quantum numbers and the relations between them. I agree, it doesn't get to the point quickly enough.
What have we got in terms of computing the energy of electrons? Not really much. In some very simple cases, you can compute wave-functions, directly for Hydrogen, or using some approximation in other cases. The easiest to understand is for nuclei with a number of electrons using a shielding parameter σ that subtracts from the nuclear charge Z. The spin-orbit interaction gives you a correction in the energy for electrons that depends on angular momentum. And the Aufbau rule is a rather empirical process of getting the ordering, and the ordering alone of the filling of orbitals.
There is no very good of computing energies for atoms with many electrons. The way that is done in atomic Physics is with self-consistent calculations using computers and that take (at least used to) months to run. Similar methods may also be used in molecular Physics/Chemistry, though I'd say, such studies have probably already been done to death.
Just to show why it's so difficult to get anywhere near accuracy, consider the small angle of the water molecule. The difference for the stretched, linear molecule is a few eV at the most. However computing wave-functions from first principles (if we could do that) all the electrons including the inner ones from Oxygen, total energies would sum up to thousands of eV. It is a very tiny difference in energy that puts an angle in the water molecule, thereby giving it a small polarity, thereby making it an universal solvent (well, almost), with all the interesting chemical properties of water.
Even the Aufbau rules, are only approximations. Sometimes orbitals do not fill completely before putting an electron at a "higher" orbital. The ground state for "chromium and copper have electron configurations [Ar] 3d5 4s1 and [Ar] 3d10 4s1 respectively, ie one electron has passed from the 4s-orbital to a 3d-orbital to generate a half-filled or filled subshell." I am quoting from Wiki http://en.wikipedia.org/wiki/Electronic_... , a very interesting entry you may want to read. Pay close notice to the part "Shortcomings of the Aufbau principle."
If you still want to follow up on issues and interchange emails about this, please do.
E.g. elements in group 1 (lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr)) will have 1 valence electron in their 'ns' orbital - Li n = 2, so it has 1 electron in the 2s oribtal; Cs will have 1 electron in the 6s orbital.
E.g.For group 15 elements (nitrogen (N), phosphorus (P), arsenic (As), antimony (Sb), bismuth (Bi)), they will have ns2 np3 valence electron configuration: so. As will have 4s2 4p3 valence electron configuration; Sb will have 5s2 5p3 configuration.
For the transition metals remember that the valence (n-1)d orbitals fill before the np orbitals. So: e.g. Sc (scandium) is 4s2 3d1 rather than 4s2 4p1; Zr (zirconium) is 5s2 4d2 rather than 5s2 4p2.
For the heavier elements and lanthanide and actinide series, it can become complicated due to relativistic effects and simple rules cease to apply.
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