Aluminum has a density of 2.699 g>cm3 and crystallizes with a face-centered cubic unit cell. What is the edge length of a unit cell in picometers?

Video transcript

Hello. Everyone in this video we're going to be solving for the edge length as well as our density of silver given that it falls A. F. C. C. Structure. So first part then let's offer our edge length. So our edge length Is equal to two square root of two times our radius. Now plugging in my radius it says it's 1:45 p. m. Close plug that in 1:45 p.m. Putting these values into my calculator. I get the edge length is 4 10 P. M. And that's going to be my first answer for this problem. Second part let's solve for the density. So density for FCC unit cell density here in green. This is going to be my formula. Alright. So also one thing to keep in mind of putting asterix off to the side is that the molar mass of silver which is going to be a G. Is equal to 107.87 g per mole. All right. And before plugging in any new yorker values. And the other thing I wanna point out Is that the atomic radius of the silver is going to be 4:10 0.12 P. M. And then in centimeters that's just four point one oh 12 times 10 to the negative eight centimeters. All right now we can go ahead and plug in some numerical values. So have d for density equal to for Adams Times 107.8 seven. Rums Permal Times 4.1012 times to the negative eight cm. And that's going to be multiplied by the guardians number. So I have six point oh 22 times 10 to the 23rd. Adams Her. Of course all the units will cuts out beautifully and we put this into the calculator. We get that density is equal to 10.4 g per centimeter. Cute, and that is going to be my final answer for this problem. So again we have the edge length of 4:10 p.m. And we have the density of silver being at 10.4 g per centimeter cubed. Alright, thank you all so much for watching. Have a great day.