So I'm going to start by drawing the BCC structure. And then 8th of an atom goes in each corner. And 1 atom is in the center. Okay. So the planar packing factor for the 1-1-1 plane is equal to the area of the atoms. On the plane, over the area of the plane. Now, the 1-1-1 plane looks like this. Alright. So let me draw it out bigger as we start examining it. Look something like that. And a 6th of an atom fits in each corner over here. What about the center? So when you're calculating planar packing factor, you have to know that whatever lies on the plane, the center of the atom must be on the plane for it to count towards the density. So if I were to look at the 1-1-0 plane, which looks like this, this is where you'd find the center of the middle one lies on the 1-1-0 plane. But if you look at it more closely, the center of the plane does not lie on the 1-1-1 plane. And so it does not count as the planar density. So that's gone. Now what's in here is a 6th. So let's count the number of atoms, which is just 3 times 1-6, which is only half of an atom. Now we need to find the area of the plane, plane. And for that, we know that it is a triangle, so it's half-based times height, times height. I'll just get rid of this. So this is our height, goes down the middle. And this is our base. This is also our base, because it is any collato triangle. Now let's calculate. We don't know either of them. We don't know h or b. So I'm going to start by calculating b. And for that, I need the bottom face of our BCC, which looks like this. This is the reduced sphere model. So don't get angry. This is a, which is 4 over root 3, this is also a. And this is our b. You can visualize that. This is what we're calculating. So let's calculate b, which is b squared is equal to a squared plus a squared. So a squared plus a squared. So b squared is equal to 2 times 4 over root 3r squared. That would mean 16 over 3r squared. OK. Let's continue. We get 16 times 2 is 32 over 3r squared. And I'll put it here. b is equal to, so root 32, 4 root 2 over 3. So actually, I'll just put root 32 over 3 within r at the side. OK. So that's our b. Now we move on to finding our h. Like in previous 1 1 1 planar packing factors, we find the h by using this geometry here, where we have this right angle triangle. So in this case, this is b over 2. I'll write that b over 2. Let's calculate h. So b squared is equal to h squared plus b over 2 squared. OK. So we have our b, which is root 32 over 3r. Let's square that. 32 over 3r equal to r squared, actually. h squared plus b over 2 squared. So it would be this all over 2 squared. So we have 32 over 3 all over 2 squared, which is 4r squared. That makes sense. And crunch the numbers. So we have all over 1. We have 32 over 3r squared. It's equal to h squared plus 32, actually 34, 32 divided by 4. Should be 8 over 3r squared. And let's put this to the other side. So 32 minus 8 is 24 over 3. 24 over 3 is 8. So 8r squared is equal to h squared. Follow my arrow. h is equal to 2 root 2r. So we have our h. We have our b. We can solve for the area of our plane. So we have h are b, which is root 32 over 3r times 2r 2r. OK. Follow this arrow. And so let's solve for this. So 2 goes out. 32 times 264 root 64 is 8. So let's see. Area is equal to 8 all over root 3r squared. Perfect. We have our area of the plane. Now we're going to put it into our planar packing factor equation. So planar packing factor. So the area of the atoms on the plane, we have half of an atom times the area of an atom, which is pi r squared. So half times pi r squared all over the area of the plane, 8 over root 3. r squared. So for that, we get root 3 pi all over 16.