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In Bohr's model, Bohr stated that the angular momentum of the electron is quantized and stated that $$L=\frac{nh}{2\pi}$$ So what is the proof for that equation or, in other words, how did he derive that equation?

Qmechanic
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Omar Ali
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    That's an assumption of the Bohr model. You can't derive it. For why angular momentum is quantized in the true quantum theory, see e.g. this question. – ACuriousMind Nov 18 '15 at 15:33
  • @ACuriousMind No it's not. It follows from the assumptions. See https://en.wikipedia.org/wiki/Correspondence_principle#Bohr_model – Praan Nov 18 '15 at 15:36
  • @Praan: "Assuming, with Bohr, that quantized values of L are equally spaced[...]" You may be able to derive that it is quantized from slightly different assumptions, but that formula is basically put in by hand. – ACuriousMind Nov 18 '15 at 15:39
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    Related: http://physics.stackexchange.com/q/28520/2451 – Qmechanic Nov 18 '15 at 15:50
  • my question is how he came up with that equation???what are exactly the caclculations that he did to come up with that equation??? – Omar Ali Nov 18 '15 at 16:06
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    I often wonder why we still teach the Bohr model... – Robin Ekman Nov 18 '15 at 16:51
  • He didn't do any exact calculations. He made an educated guess about whether $L$ would be quantized and how. I'm not aware of any contemporaneous notes which Bohr made about why he made that particular guess. He may have made several before he found a form which gave the proper wavelengths for the emission spectra. @RobinEkman I think we teach it because it shows how scientists attack a "frontier" problem, and end up with a partially right, yet wrong answer. – Bill N Nov 18 '15 at 19:44

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In a sense this is an assumption, however it's an assumption that has a basis in the history of QM at the time. I attach images of four pages from http://www.amazon.com/Einstein-Quantum-Quest-Valiant-Swabian/dp/0691168563, which I'm currently reading and recommend if you're interested in the history, that give something of the flavor. Chapter 20, Page 172-3 Chapter 20, Page 174-5 Bohr can be said to be working by analogy with what Planck and Einstein had done and found to work for the electromagnetic field. What Bohr did was justified more by how well the implications of his assumption matched up with experimental results than by how beautiful the assumption was. It's not until de Broglie that the idea that Bohr puts into the mathematics here becomes matter waves, resulting in the Schrödinger equation etc., etc.

Peter Morgan
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