Let's consider the simplest possible example, $\mathrm$ to predict anything with it you have to define what the forces are. Why? Because all you really need is the legal-number-combinations rules, not the way it's derived from the Schrödinger equation. The short answer to your question is that when we transition from quantum numbers for electrons in monatomic allotropes of an element to the analogous treatment of a molecule, the way the pattern of legal orbitals transforms is the same as would be expected on a classical model. The Bohr lie would be that the electrons living in these orbitals have a precise location, and that orbitals form so as to get the electron count in each atom's outermost shell right and make for a stable molecule - you know, the usual $8$-electron rule (or $2$ for hydrogen, since it's trying to be like helium, not neon). Like atomic orbitals, $\pi$ MOs hold at most 2 electrons (let's not get into $\sigma$ bonding for the moment). The applications of Bohr-like reasoning you've brought up concern molecular orbitals, and these are a slightly more advanced topic at this point I wish I knew what chemistry undergrads are taught about them, but I imagine Peter Atkins explains MOs with much the same rigour. When physicists teach undergraduates enough quantum mechanics to do the hydrogen atom properly, electrons end up in specific atomic orbitals due to their quantum numbers, and each orbital can hold at most 2 electrons. Going beyond that, how does an "electrons are somewhere specific" approximation lead to useful models of sharing and transferring electrons in covalent, ionic and metallic bonding? Well, we'll focus on covalent for now. The linked article discusses the Bohr model, but leaves some of your sub-questions unanswered. This is an example of the "correspondence principle" in the broadest sense, that new theories should explain why old ones got some things right. Also does a lot of chemistry stuff quite well (as suggested in the original question) but I'm not a chemist so can't praise the model for that. The Bohr radii for various energy levels turn out to be the most probable values predicted by the Schrodinger solutions.Ĭ. In particular, one deduces the right value of the Rydberg constant.ī. Correct energy spectrum for hydrogen (although completely wrong even for helium). It predicts a single "radius" for the electron rather than a probability density for the position of the electron.Ī.In particular, because of angular momentum degeneracies, the spin-orbit interaction is incorrect. It doesn't hold well under perturbation theory.Most obvious is the ground state, with has $\ell=0$ in Schrodinger's theory but $\ell=1$ in Bohr's theory. In particular, it doesn't have the right angular momentum quantum numbers for each energy levels. This number can be seen through Zeeman splitting. It incorrectly predicts the number of states with given energy.Essentially, how good the Bohr model is as a diagram, as a tool for learning, and as a tool for simulation. If not, I'm wondering what an alternative model is that is better for simulation. If you build a computer simulation of atoms with the Bohr model, I'm wondering if it would be "accurate" in the sense of modeling atomic phenomena, or is it not a good model to perform simulations on. So I'm wondering what the inaccuracies are, and if there is a better way to understand them than the Bohr model. What I'm wondering is, if the Bohr model is used essentially throughout college education in the form of these diagrams, it seems like it must be a pretty accurate model, even though it turns out atoms are more fuzzy structures than discrete billiard balls. However, in chemistry education like organic chemistry you still learn about chemical reactions using essentially diagrams that are modified lewis structures that take into account information about electron orbitals: However, electron orbitals were found to be less rigid and instead be fuzzy fields which, instead of being discrete/rigid orbits, look more like: And it works pretty well as seen in the Lewis structures: This allowed for chemists to find a model of chemical bonding where the electrons in the outer orbits could be exchanged. The Bohr model of the atom is essentially that the nucleus is a ball and the electrons are balls orbiting the nucleus in a rigid orbit.
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