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Transcript
Transcript 05-4 Definite Uncertainty A few introductory words of explanation about this transcript. This transcript includes the words sent to the narrator for inclusion in the latest version of the associated video. Occasionally, the narrator changes a few words on the fly in order to improve the flow. It is written in a manner that suggests to the narrator where emphasis and pauses might go, so it is not intended to be grammatically correct. The Scene numbers are left in this transcript although they are not necessarily observable by watching the video. There will also be occasional passages in blue that are NOT in the video but that might be useful corollary information. There may be occasional figures that suggest what might be on the screen at that time. 401 Avatar4-MoreUncertainty DIANA: Schrödinger’s Equation is really cool! CHAUCER: Yes it is, Diana. KEVIN: I agree, but can we talk a little more about Heisenberg’s Uncertainty Principle? Isn’t there more to consider than the approach we used to describe it? CHAUCER: Certainly Kevin – Jeeves, let’s have a closer look at that please. 405 More Uncertainty JEEVES: Werner Heisenberg did more than make a QUALITATIVE statement when he said that a particle’s position and momentum could not be known simultaneously … He wrote an equation that QUANTIFIED the relationship. Let’s see how that information can lead to an easy understanding of the hydrogen atom described in exquisite detail by the Schrödinger Equation. Without going into too much detail let’s look at a proton and an electron. Since the electron has a very tiny mass, it can occupy a very large region of space. Conversely the proton has a large mass, 2000 times that of the electron, and therefore it occupies a very tiny region of space. The result is the Quantum Mechanical hydrogen atom… A tiny massive nucleus surrounded by a much larger cloud representing the electron. If we look at a simple graph relating the probability of finding the electron in a shell at a given distance from the nucleus, we find that as we travel outward from the nucleus, the probability increases at first as the shell expands. It reaches a maximum value and then decreases again as the electron cloud thins to almost nothing at large distances. Amazingly, the radius where the probability reaches a maximum is precisely equal to the radius of the first allowed orbit of Niels Bohr ‘s model of the hydrogen atom. And it’s energy is exactly equal to the energy of an electron in this orbit in the Bohr atom. So this is a VERY good picture of a hydrogen atom with the electron in the lowest energy state. The electron occupies a cloud instead of an orbit, but it spends most of its time at the radius predicted as an orbit by the Bohr model. AND it spends most of its time possessing the energy that an electron in that orbit would have. 410 Excited States But of course, the atom is not always found in this lowest energy state. As there are other orbits allowed in the Bohr model, there are other, higher energy states in the quantum mechanical hydrogen atom. These states are defined primarily by the quantum number “n” that we talked about earlier. And for each state, the electron has a different energy which results from the shape of the electron cloud. For n=1, called the ground state, the shape is a symmetric cloud…the same in all directions. For n=2, the shape can take on two forms although both shapes have the same energy… One is a double spherical cloud – one sphere inside the other. While the other shape for n=2 is in the shape of a dumbbell For other values of n, the shapes can be pretty strange… Like this torus PLUS dumbbell shape. 415 Spectral Lines An electron in the lowest energy shell in an atom can be struck by and absorb the energy of a photon giving it enough energy to jump to the next energy shell. And the reverse process allows the electron to jump back down into the lowest energy shell and emit a photon. The color of the photon depends on the energy difference between the two shells. This explains the spectral lines that identify an element. Since white light contains all the colors in the spectrum, when we shine white light on a sample of an element under the right conditions, The atoms absorb all of the photons that allow their electrons to jump to other energy shells. SO the absorption spectrum is all the colors in white light minus those that match the difference in energy shells within the atom. And when those electrons spontaneously jump back down to the lowest energy levels, that emission spectrum contains only those lines that match the difference in energy shells within the atom.