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?
$\begingroup$
$\endgroup$
7
-
9$\begingroup$ 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. $\endgroup$– ACuriousMind ♦Commented Nov 18, 2015 at 15:33
-
$\begingroup$ @ACuriousMind No it's not. It follows from the assumptions. See en.wikipedia.org/wiki/Correspondence_principle#Bohr_model $\endgroup$– PraanCommented Nov 18, 2015 at 15:36
-
$\begingroup$ @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. $\endgroup$– ACuriousMind ♦Commented Nov 18, 2015 at 15:39
-
1$\begingroup$ Related: physics.stackexchange.com/q/28520/2451 $\endgroup$– Qmechanic ♦Commented Nov 18, 2015 at 15:50
-
2$\begingroup$ I often wonder why we still teach the Bohr model... $\endgroup$– Robin EkmanCommented Nov 18, 2015 at 16:51
|
Show 2 more comments
1 Answer
$\begingroup$
$\endgroup$
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.
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.
answered Nov 18, 2015 at 16:43