00:01
Okay, so we want to show that the first three terms of the infinite series will give us a value for alpha.
00:09
So let's notice that the first potential energy are the nearest neighbors of the six negative chlorine ions, and they're at a distance r.
00:18
So u1 will be negative 6 k e squared over r.
00:32
The second nearest neighbors are 12 positive sodium ions at a distance root 2r.
00:40
So we have 12 positive sodium ions at a distance root 2r.
00:50
And the third nearest neighbors are 8 negative chlorine ions at a distance root 3r.
01:02
This is 8 k2 squared.
01:07
Or 3r.
01:08
So the total potential energy is u1 plus u2 plus u3.
01:19
Notice that they all have k e squared over r in common, so we can pull that out.
01:31
So this gives us negative k e squared over r.
01:39
We're going to mean to actually pull up the negative as well...