- #1

Dick Niggle

- 10

- 0

I always used the matter-wave as an explanation for why the electron does not crash into the nucleus. As a standing wave, how could it? The wave would have to increase in frequency, almost infinitely, until it was the size of a point, the nucleus, which seemed like an impossible task.

However, using De Broglie's wavelength to explain this failed miserably. My goal was to simplify the situation as much as possible. So, we will look at just a lone Bohr's model of the hydrogen atom in an empty void of space.

I computed the wavelength of the electron orbiting at the Bohr's radius after finding it's velocity using a few formulas and simple algebra and obtained about 0.5 nm. The electron's wavelength is pretty small.

When trying to compute the wavelength of the proton, I expected that I could somehow arrive at 0 or a very small number that I could explain as insignificant, but the proton's wavelength is larger than the electron's wavelength and approaches infinity.

The electron is bound to a very high speed around the proton, so no matter what, it's wavelength becomes very small. The proton, however, is stationary, even to the perspective of the electron. So, somehow it has an infinite wavelength and shouldn't even be there.

If I decide to give the atom some velocity, both the proton and the electron waves decrease in length, because this extra velocity is being added to the electron, too. So, it seems, no matter what, the proton has a considerably greater wavelength than the electron.

Why is this so? Can you not describe more than one object at a time with De Broglie's wavelength? Are the proton and electron wave function somehow intertwined? It appears that the matter-wave no longer explains why the electron does not crash into the nucleus for me. I have looked and looked for an answer to that, but none sufficed. I suppose I will never understand. How do I fix this problem so that there can be a standing wave orbiting a solid nucleus like my textbook described.

However, using De Broglie's wavelength to explain this failed miserably. My goal was to simplify the situation as much as possible. So, we will look at just a lone Bohr's model of the hydrogen atom in an empty void of space.

I computed the wavelength of the electron orbiting at the Bohr's radius after finding it's velocity using a few formulas and simple algebra and obtained about 0.5 nm. The electron's wavelength is pretty small.

When trying to compute the wavelength of the proton, I expected that I could somehow arrive at 0 or a very small number that I could explain as insignificant, but the proton's wavelength is larger than the electron's wavelength and approaches infinity.

The electron is bound to a very high speed around the proton, so no matter what, it's wavelength becomes very small. The proton, however, is stationary, even to the perspective of the electron. So, somehow it has an infinite wavelength and shouldn't even be there.

If I decide to give the atom some velocity, both the proton and the electron waves decrease in length, because this extra velocity is being added to the electron, too. So, it seems, no matter what, the proton has a considerably greater wavelength than the electron.

Why is this so? Can you not describe more than one object at a time with De Broglie's wavelength? Are the proton and electron wave function somehow intertwined? It appears that the matter-wave no longer explains why the electron does not crash into the nucleus for me. I have looked and looked for an answer to that, but none sufficed. I suppose I will never understand. How do I fix this problem so that there can be a standing wave orbiting a solid nucleus like my textbook described.

Last edited: