What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

Video transcript

everyone in this video. Recounting how many items there are in a face centered cubic unit cell. So the number of atoms in a unit cell has its formula which is an It goes to end of I. Plus and of F divided by two Plus End of C. divided by eight. Let's break this down. So this end of I. That means the interior atoms than our end of F. That's defeats Adams. And if you can guess and if seat is our corner atoms. All right. So let's go ahead and try to draw out our face centered cubic unit cell. Alright, so first let's go ahead and draw our cube. I just like to always have a visual representation. Try my best to draw a cute three D cube. All right. So will have and Adam here here here and here. Course the other corners as well. So we can see here that we have a total of eight corner adam. So it's just M. C. Then let's go ahead and find the these Adams. So face Adams of one two three for five. And See Where's The 6th 1? Mhm. Six. So have six N. F. Then our interior atoms. That's going to be able no. So You have zero. And so again, following this formula then we'll get and because zero plus in parentheses and F. Six divided by two NFC is eight divided by eight. Now get 65 x two is 3. A device. It is one. So and equals to four. So how many ends are there in this face? Inner cubic cell cubic unit Some is going to be four atoms, and this is going to be my final answer for this problem. Thank you all so much for watching.