This provided the Bohr theory with a solid physical connection to previously developed quantum mechanics. That is, the circumference of the circular Bohr orbit is an integral number of de Broglie wavelengths. Louis de Broglie's theory of matter waves predicts the relationship between momentum and wavelength, so Where \(p\) is the linear momentum of the electron. One can write the angular momentum quantization condition as They don't really have a color, we just use that idea because it's sort of helpful, just like using the idea of positive and negative for charges is helpful.\).Īlong with this excellent agreement with observation, the Bohr theory has an appealing esthetic feature. IN the field of quantum chromodynamics, we say that particles have a color. It's just the name that we've given a quark that has certain properties. There's nothing unusually strange about the strange quark. There's a charmed quark and a strange quark. THere's nothing "up-ish" about an up quark. "Up" and "down" don't have any meaning other than to identify the type of quark. A quark can be an up quark or a down quark. We’ll use a Bohr diagram to visually represent where the electrons. We have other properties like this for other particles. In this video well look at the atomic structure and Bohr model for the Hydrogen atom (H). It's just a characteristic that particles have or don't have, and we know what the effect is of having or not having that property. "What is spin" doesn't have any deeper answer than does the question "what is charge". But there is no point in trying to answer "what is electron spin" by referring to some familiar object like a ball or a planet, because electrons are not balls or planets, they are their own thing, and you just have to accept that they have a property whose effects we understand very well, and we happen to have named it spin. Still, they have a property that works sort of like an orbit (orbitals) and they have a property that works sort of like rotation about an axis (spin). Using this concept actually helped a bit, just like Bohr's imagination of little orbits helped a bit, but again, the electrons are not like little planets: they don't revolve around the nucleus, and they don't rotate on their axes. Just as Bohr imagined that the atoms were little planets revolving around the nucleus as though it were a sun, other scientists tried to extend that idea by imagining that the little planets, just like real planets, had spin. It got named spin back when people were working with the Bohr model and trying to extend it to atoms beyond hydrogen. Spin is just a property that electrons (and other particles) have. For another layer, you can take the fact that you can never cool anything down to exactly 0K (-273.15C) (although you can get close) and so nothing will ever have 0 velocity. (1 value in a range of reals is like trying to throw a dart at a dartboard with an infinitely thin wire and hitting the wire). With this uncertainty, the velocity is almost definitely not 0. As we can't physically measure to perfect accuracy, there is an uncertainty in both measurements of the degree that we know it's probably stationary and it's probably 'over there'. Thus, only certain fixed orbits are allowed. Even though it is very different from the modern description of an atom, it is. The model proposed in 1913 by the Danish physicist Niels Bohr (and later further developed by Arnold Sommerfeld) to describe the hydrogen spectrum was of great importance in the historical development of atomic theory. Thus, an electron can move only in those orbits for which its angular momentum is an integral multiple of h/2. 7.4: The Bohr Model of Hydrogen-like Atoms. The angular momentum of an electron in a given stationary state can be expressed as mvr n h n × h 2. So, if you know with 0 uncertainty what the velocity is, then you have no idea where it is, and all future involvement of the particle is pretty much irrelevant (how is the electron going to diffract around an atom if the electron is in a different galaxy?). This expression is commonly known as Bohr’s frequency rule. The square (probability function) shows that it has an equal chance of being anywhere. If you take the infinite wavelength interpretation, then it would be nearly 0 (1/inf) but constant everywhere. Isn't to do with the fact that the velocity is not quite 0? if you know it is exactly 0 then the uncertainty in the position is infinite as well (momentum is a function of velocity, so delta P = 0 -> delta V = 0 -> delta X = inf) therefore it has an equal probability of being anywhere.
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