## Schrodinger's Equation [ENDORSED]

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Kellina Tran 2I
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### Schrodinger's Equation

Can someone please summarize the key points of section 2.1? I am confused about the relationship of Schrodinger's equation to wave functions and orbitals.
Also, on the outline, what does it mean by the interpretation of atomic orbitals in terms of probability?
Sorry that's quite a few questions, but thanks in advance!

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### Re: Schrodinger's Equation  [ENDORSED]

The wavefunction is the mathematical expression that contains all the info about the quantum system, for example, the electron bound to the nucleus, then by applying the Hamiltonian operator, you get an expression for total energy of that electron. This full expression is called the Schrodinger equation. Further operations on the result can give information about the orbital shape itself (related to the angular momentum).

The interpretation of atomic orbitals in terms of probability is best explained through an example of repeated observations of the electron in the orbital. If you made one observation with very low angular momentum certainty but high position certainty, for example in the case of a hydrogen atom, you would see the electron just as a dot somewhere away from the nucleus. Then, if you repeated that same experiment many times, you would eventually see that the orbital is a sphere with a definite distance away from the nucleus. Some experiments would locate an electron even farther away than most of the others, but the probability of this happening is very low. Conversely, the probability of finding the electron at a distance equal to the "atomic radius" away from the nucleus is very high. You can even imagine this experiment for another element with an electron in the p orbital. It is only after a similar set of experiments that you would even know the p orbital is bi-lobed with a node in the center. There would be some experiments with an electron found way out of this shape, but the probability of that happening would be very low.

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