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I was told by my teacher about the Bohr model of atoms. He assumed that the electrons are associated with definite energy levels

I just don't understand why that specific energy level makes them more stable than other levels.

Later the model was replaced by the quantum mechanical model which is based on finding the probability of occurrence of electrons in certain regions.

I don't understand why the probability of finding an electron is greater in the region where it is greater.

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Bohr's essential point was that since an electron has some wave-like characteristics, then if it is in orbit around a nucleus any such orbit must consist of an integer number of wavelengths- and those then were the only orbits that could possibly exist. Since energy is associated with waves, then each possible orbit would correspond to a certain specific and definite energy level. This is probably what your teacher was getting at.

Bohr's "old quantum" model was a tremendous breakthrough, but it was too simple to account for anything bigger than a hydrogen atom, and it relied on a notion of "orbit" that didn't make physical sense.

The more complex, "new" quantum model that replaced it allowed the calculation of the same definite energy levels but it did away with the idea that the electron orbited the nucleus in a precisely-defined path like a planet orbiting the sun. Instead, those precise orbits (which did not actually exist) were replaced with maps of where an electron with a certain definite energy might be found, on average- and those mapping shapes do actually correspond to the way that electrons get fitted into the volume surrounding the nucleus, while keeping out of each other's way.

The key idea behind those "cloudy" orbital shapes was that for objects as small as electrons, their precise position and momentum at any instant cannot be known simultaneously (which would necessarily be the case for a "solar-system"-like orbit model); the best that quantum physics lets us do is to know averages instead.

So, on average, the cloud shape tells you where you are most likely to find an electron, and the "denser" the cloud, the greater the likelihood that the electron is somewhere in that region at some instant in time.

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  • $\begingroup$ Nice answer. +1 from me. $\endgroup$
    – Gert
    Commented Jul 3, 2021 at 20:57

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