The standing-wave pattern with the longest possible wavelength has $\lambda=2L$, corresponding to a superposition of two traveling waves with momenta $p=\pm h/2L$. The electron is a wave, and when it's confined to a space like this, it's a standing wave. Suppose an electron is confined to a region of space with width $L$, and there are impenetrable walls on both sides, so the electron has zero probability of being outside this one-dimensional "box." This box is a simplified model of an atom. We have the de Broglie relation $|p|=h/\lambda$, where $p$ is the momentum of an electron, $h$ is Planck's constant, and $\lambda$ is the wavelength of the electron. We have to completely abandon the idea that subatomic particles have well-defined trajectories in space. For a sophisticated discussion, see this mathoverflow question and the answers and references therein: Īt the very simplest level, the resolution works like this. The quantum-mechanical resolution of this problem can be approached at a variety of levels of mathematical and physical sophistication. The Bohr model, which was an early attempt to patch up the planetary model, is also wrong (e.g., it predicts a flat hydrogen atom with nonzero angular momentum in its ground state). My question here is whether the planetary model itself addresses these concerns in some way (that I'm missing) For example, the planetary model of hydrogen would be confined to a plane, but we know hydrogen atoms aren't flat. There are even simpler objections of this type. If electrons are zooming around in orbits, how do they suddenly "stop" to form bonds. I can't reconcile the rapidly moving electrons required by the planetary model with the way atoms are described as forming bonds. What you've given is a proof that the classical, planetary model of the atom fails. Even if the electron actually orbits the nucleus, wouldn't that orbit eventually decay? ![]() ![]() I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Macroscopic forces, like those due to classical electric and magnetic fields, are limiting cases of the real forces which reign microscopically. Quantum mechanics is accepted as the underlying level of all physical forces at the microscopic level, and sometimes quantum mechanics can be seen macroscopically, as with superconductivity, for example. If you study further into physics you will learn about quantum mechanics and the axioms and postulates that form the equations whose solutions give exact numbers for what was the first guess at a model of the atom. ![]() It also explained the lines observed in the spectra from excited atoms as transitions between orbits. The Bohr model was proposed to solve this, by stipulating that the orbits were closed and quantized and no energy could be lost while the electron was in orbit, thus creating the stability of the atom necessary to form solids and liquids. One of the reasons for "inventing" quantum mechanics was exactly this conundrum. The electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus. You are right, the planetary model of the atom does not make sense when one considers the electromagnetic forces involved.
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