Two patterns of packing for two different circles of the same size are shown here. For each structure (b) determine the angle between the lattice vectors, g, and determine whether the lattice vectors are of the same length or of different lengths; (i)

(ii)

Video transcript

Hi everyone for this problem. It reads consider the two packing patterns, identify the angle between the lattice vectors. Okay, so this is what we want to do and taking a look at our two packing patterns, we can go ahead and identify what type of polygon we have. Okay, so for the first one we have a square and for the second one we have a hexagon. Okay, there are different types of lattices. And so these are the two that we're working on today for this problem. And in order to solve this problem, we need to know that for any regular polygon, the angle is equal to N -2 times 180° divided by N. Where N is equal to the number of sides. Okay, so for the first one, let's go ahead and do that one. So for the first one we have a square. Okay, and with this square N equals four. So let's go ahead and figure out the angle by using our equation. Okay, so that means our angle is going to equal for minus two times 180 degrees divided by four. So this gives us an angle of 90 degrees. Okay, now, for the second one let's go ahead and do that, we have a hexagon. Okay, so for a hexagon, there is N. equals six. So when we saw for the angle we have six minus two times 100 and 80 degrees divided by six. And this gives an angle of 120 degrees. Okay, so we just identified the angle between the lattice vectors, we have 90 degrees for the square and degrees for the hexagon. Okay, so this is the answer to this problem, and this is the end of this problem. I hope this was helpful.