Time-averaged position of 1s electron

Hi, where do you think a 1s electron will be in an atom?

“On a circle around the nucleus, of course!”
(or “Euh… I don’t know”)

No, quantum mechanics is more fun! First of all, the nucleus and the electron cloud are the same in every direction of space. Not only to the left and right, but also to above and below. We can say that it is spherically symmetric.
Next, I have to tell you that the distance between the nucleus and the electron is not fixed, like it is on a circular orbit. Actually, the electron can be everywhere. It can even be in Brussels while we’re standing here in Harelbeke, but that is very unlikely. There is indeed a ‘most probable distance’, which means that the electron spends most of its time at that distance from the nucleus. It is this distance you know as the circular orbit, but now you know that this should be a spherical shell.

“So I was right that the average position of the electron is at a definite distance from the nucleus?”

Yes and no. What you were thinking about is the most probable distance, which I just explained. But as I’ve told you, the electron can also be in Brussels. This means that, on average, the electron will be further away from the nucleus than the most probable distance. Imagine coming once in a while very close to the nucleus, and once in a while going very far away. You can go much much farther away than that you can come close, so on average you will be further away.

“Okay interesting, I think I understand it a little bit.”
(or “Pffff, boring!”)

There is one more thing I have to tell you. The electron will be equally likely on the left as on the right, as well as below or above. So these will cancel each other, and in the end, the time average position of the electron will be right at the center of the nucleus.

“Now you are joking! I don’t believe that!”