Rhodium has a density of 12.41 g/cm3 and crystallizes with the face-centered cubic unit cell. Calculate the radius of a rhodium atom.

Video transcript

Hello. Everyone in this video we're trying to determine the radius of our radium adam. So let's recall F. C. C. Unit cell, the atomic radius. So eight is going to be two square root of two times the radius and our density. So deep is going to be this right over here. Alright so the molar mass of the radium. So just I. R. Is equal to 1 92. g per mole. Now let's go ahead and solve for our density. So we'll have the the 4M divided by two skirt of two are all this is going to be cute times And a and again just simplifying this a little bit. We'll get 16 square root of tube and our which is radius cubed of N. A. Now just solving for r cubed We'll get em over four squared of two ton of density and eight. Now putting in numerical values now We get our cubed equals two. Well we have that four atoms And then we have 192.22 g per mole. It's going to be all over the 16 squared or two times 22.4 g times centimeter squared. Of course we're going to go ahead and multiply by avocados number 6.022 times 10 to the 23rd power adam. Hm. Now just simplifying everything and putting all these numerical vise into a calculator. I'll get the value of 2. Times 10 to the -24 power centimeter cute. Now just scrolling down a little bit. I want to go ahead and square it square root this to kind of isolate R r the radius. So if we do that and putting that into my calculator, I will get the value of 1.36 oh eight times 10 to the negative eight of course, same unit. And I'm gonna go ahead and convert this to a different unit. So 1 36 PM. Technically both answers are correct, but this is going to be my finalized answer for this problem. Thank you all so much for watching.