Smeared out Electron & Quantum Mechanics

In the top of this page where I discuss the problems and solutions, I said that electrons move in circular orbits around the nucleus. This statement isn’t entirely correct, see electron aren’t as depicted in some elementary text books, little balls flying around the nucleus and there’s a lot of empty space between them. In fact there aren’t any empty space at all around the nucleus, the electrons occupy it all. This is because the electrons wave function is “smeared” out around the nucleus and the electron has a chance of existing a bit everywere, which also has to do with the uncertainty principal. Infact the electron doesn’t just have a chance of being somewhere around the nucleus, it has a small but existing probability of being on Pluto or another galaxy even. So does that mean that we can forget the notion of an electron and also the notion of neat orbits around the nucleus? Not really, there are things called orbitals which are volumes of space around the nucleus were the electron has an about 90% chance of being found. Here are some pictures to show you what an orbital might look like:

Imagine the nucleus being in the centre of the shapes.

Now you might wonder if a electron really can form a standing wave around sucha strange shape. The answer is that it doesn’t have to adapt to the orbital, but infact it’s the wave functions that arise from treating a electron as a standing wave which leads to the orbitals. But they aren’t cicular as in the Bohr model, so then we can say bye bye to having nice division of the areas were the electron can be and not? Again not really, even though they aren’t circular it’s still largely a division of the areas were the electron can be, although it can as said above be anywhere. But since 90% of it’s wave function(E.i it has a 90% chance) is within these orbitals it’s still a division which keeps the electrons in place and the atoms functioning

As seen above the orbital can take on different shapes, what shape the orbital has depends on the energy level of the electron or more specific on the three first quantum numbers. There are four quantum numbers:

The principal quantum number.In what shell around the nucleus the electron is.n
The orbital quantum number.In what sub shell(there are shells within the normal shells) the electron is.l
The magnetic quantum number.What energy level in the sub shell the electron has.m
The spin quantum number.What spin the electron has. Can only have two values: +1/2 or -1/2s

(You shouldn’t care if you don’t understand the table I mainly put it there for curiosa.)
There can be two electrons in one orbital, but only if they have the opposite spin.

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