The Wave Nature of Matter

 I'm actually relieved to hear that this Bohr stuff isn't the end of the story. The mathematical part of the Bohr model makes sense to me, but some of its assumptions seem pretty arbitrary. I mean, why should an electron's angular momentum have only certain values? And why do electrons emit or absorb radiation only when they jump between energy levels? I know Bohr's theory fits a lot of experimental results, but it doesn't really explain why atoms behave the way they do.

If we begin to think of electrons as waves, we'll have to change our whole concept of what an "orbit" is. Instead of having a little particle whizzing around the nucleus in a circular path, we'd have a wave sort of strung out around the whole circle. Now, the only way such a wave could exist is if a whole number of its wavelengths fit exactly around the circle. If the circumference is exactly as long as two wavelengths, say, or three or four or five, that's great, but two and a half won't cut it.

So there could only be orbits of certain sizes, depending on the electrons' wavelengths --which depend on their momentum.

Fitting Waves Around a Circle

Click and drag on the circle to change the circles radius.

Or drag the grey ball around to change the length of the wave.

When an exact number of wavelengths fits around a the circle, the waves will be green. Otherwise they are red.

See how the wave only fits at certain "orbits"?


Exactly. And if you do the algebra--set the wavelength equal to the circumference of a circle--you'll get precisely the condition that Bohr used: an electron's angular momentum must be an integer multiple of h bar.

So how come when I look at a bowling ball, I don't notice it acting in a wavelike manner? You said that everything is affected by wave/particle duality.

Think about what the wavelength of the bowling ball would be. According to de Broglie, the wavelength is equal to Planck's constant divided by the object's momentum; Planck's constant is very, very, very tiny, and the momentum of a bowling ball, relatively speaking, is huge. If you had abowling ball with a mass of, say, one kilogram, moving at one meter per second, its wavelength would be about a septillionth of a nanometer. This is so ridiculously small compared to the size of the bowling ball itself that you'd never notice any wavelike stuff going on; that's why we can generally ignore the effects of quantum mechanics when we're talking about everyday objects. It's only at the molecular or atomic level that the waves begin to be large enough (compared to the size of an atom) to have a noticeable effect.

If electrons are waves, then it kind of makes sense that they don't give off or absorb photons unless they change energy levels. If it stays in the same energy level, the wave isn't really orbiting or "vibrating" the way an electron does in Rutherford's model, so there's no reason for it to emit any radiation. And if it drops to a lower energy level... let's see, the wavelength would be longer, which means the frequency would decrease, so the electron would have less energy. Then it makes sense that the extra energy would have to go someplace, so it would escape as a photon--and the opposite would happen if a photon came in with the right amount of energy to bump the electron up to a higher level.