# Neils Bohr Model

1. Aug 5, 2014

### Yashbhatt

Recently, I saw a video on Introductory Quantum Mechanics. Here's the link : https://www.youtube.com/watch?v=5Gnqpbge3Yk

I failed to understand the explanation of de Broglie's model. He mentions that the waves interfere with each other but how do we know the properties like amplitude etc. of those waves and what does he mean by the "the wavelengths calculated for the electron". Does it relate to the amount of potential energy an electron has?

2. Aug 5, 2014

### Staff: Mentor

There is plenty of stuff explaining the Bohr model eg:
http://en.wikipedia.org/wiki/Bohr_model

But, yes if looked at carefully it is confusing.

That's because these early models were not really correct and it shows up if you push it too far.

The situation was very chaotic with all sorts of ad-hoc rules invented by Summerfeld and others to try and save the situation. It failed. A breakthrough was required. That came when Schroedinger and Heisenberg developed two very different formulations that fixed it up - wave mechanics and matrix mechanics respectively. And although not usually mentioned a guy called Dirac also had one that was much more elegant based on what's called q numbers. Three separate theories - not good. Then Dirac developed what was known as the transformation theory that tied them all together and was very elegant. Its basically what we call QM today.

That being the case the stuff you are talking about is basically of historical interest. My advice is forget about it. Study the conceptual core of QM:
http://www.scottaaronson.com/democritus/lec9.html

Once you have digested that do a separate post and myself and others can explain how that conceptual core explains the hydrogen atom. But basically, its a surprising fact, that only comes out with advanced math, if we want those probabilities to not depend on our coordinate system then this leads to the Schroedinger equation:
http://en.wikipedia.org/wiki/Schrödinger_equation

And when you apply it to the Hydrogen atom low and behold it explains all those funny things the Bohr model had trouble with such as exactly why it only had certain energies:
http://www.ciul.ul.pt/~ananunes/QM/Laguerres&Hydrogenatom.pdf [Broken]

Don't be worried if the math beats you - simply try to get the gist.

Thanks
Bill

Last edited by a moderator: May 6, 2017
3. Aug 5, 2014

### Yashbhatt

You are correct but I was thinking that Niels Bohr must have thought some thing. What I din't get is what his theory explained and what it din't. It is interesting to know how the theory was developed over time.

4. Aug 5, 2014

### stevendaryl

Staff Emeritus
In classical physics, an electron orbiting around a proton in a circular orbit would have energy E and angular momentum L related by:

$E = - \dfrac{m q^4}{2 L^2}$

where $m$ is the mass of the electron, and $q$ is the charge of the electron.

Bohr's hypothesis was that the angular momentum can only be an integer multiple of $\hbar$. So his model predicted that the allowed energy levels of a hydrogen atom are

$E_n = - \dfrac{m q^4}{2 \hbar^2 n^2}$

where $n$ is any positive whole number.

It was a completely ad hoc proposal, although it was later given a sort-of justification in terms of de Broglie's suggestion that electrons, besides being particles, have an associated wave. Then de Broglie's idea inspired Schrodinger to come up with his wave equation. (I think Heisenberg's version of quantum mechanics wasn't much influenced by de Broglie.)