00:01
To describe where an electron is, in an atom, we only discuss the probability of this electron.
00:06
And as the electron moves a distance from the nucleus, the probability changes.
00:13
And so when we talk about this, we can look at three different distances from the nucleus in terms of a constant called a -not.
00:21
So first we'll look at the probability of finding an electron at the actual distance, a -0 from the nucleus, and then a half that distance and then four times that distance.
00:33
To solve for probability, the equation 4 pi rd times si square is huge.
00:40
4 pi rd talks about the volume of the sphere that we're using to describe where the electron is.
00:49
And si squared is the wave function corresponding to a particular electron.
00:54
Psi is equal to 1 over constants pi a0 cube to the half times e raised to the r over a0.
01:05
A .0 is a constant, which is 52 .9 picometers.
01:11
D is the thickness of the shell, which in all of these examples will be one picometer, and r is the variable that changes or the distance from the nucleus.
01:21
While these are all in picometers, we don't need.
01:24
To change them to meters because the units will cancel out.
01:29
We calculate the probability that r equals a0 or 52 .9 pica meters, it'll be 4 pi times 52 .9 squared times 1 times 1 over pi times 52 .9 cubed.
02:07
And then the square root of that value times e to the minus r, 52 .9, over a0, 52 .9...