The density of an unknown metal is 12.3 g/cm3, and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal

Video transcript

Hello everyone in this video. We're trying to calculate the molar mass of the unknown metal. So first for any F C C. Unit cell, the atomic radius. So It's going to be two times the square root of two times the radius. And the density so deep Is equal to four M. Divided by a to the 3rd and eight. All right. So separating this information are these formulas here. Then my density again. Just using my formula. We're plugging in our a to this day here two square root of two times radius. It's cute. Now kind of simplifying this again for Then we'll get six. Sorry divided by Our 16 square root of two and the rate is going to be cubed Times that an eight. No for our m then we'll have such a salary for em here from here We'll get that. It's going to be 16 squared of two times. Multiply that by the radius cubed and in all divided by four Adams. All right. Now expanding this a little bit more numerical values. We have 16 square root of two. I'm going to multiply that by 8.96 g time set and reader cute. And this is dead. See you got over here then you'll have The conversion so have 0.12. So it's and times one cm To 10 to the 7th. And um to convert it to centimeters are going to be cute. Then continuing on Will have 6.22 Times 10 to Adams. Mm. No the lashes avocados number. Right. And of course all that is going to be divided By our four atoms. So we have this here. Just plugging all the values in now. We'll just get this right. So plugging everything into my calculator. Then I'll get that. The smaller mass of my unknown medal Is equal to 63.7 g more. And of course, grams per mole is going to be a very common unit for more mass. So that's also an indication that we got this answer, correct? Alright, This is going to be my final answer. Thank you all so much for watching.