An element crystallizes in a face-centered cubic lattice. The
ed...

Question

An element crystallizes in a face-centered cubic lattice. The 
edge of the unit cell is 4.078 Å, and the density of the crystal 
is 19.30 g>cm3. Calculate the atomic weight of the element 
and identify the element.

Accepted Answer

Hello everyone in this video. We're trying to identify the element by the atomic weight given the density and the edge of the unit cell. So we want to go ahead and also assume that the element crystallizes in a face centered cubic lattice. Alright, so first things first is that we're going to calculate the volume of the unit cell. Okay, so how to do that is we're gonna go ahead and take the edge of the unit cell. Were just given to us in the problem as 4.08 Angstrom. So how that And then we're gonna go ahead and convert this into centimeter cute. We don't have a direct conversion from action to cm or centimeter cubed but we do have a conversion for action two cm. That being for every one ancient Is going to be 1. times 10 to the negative eight cm. And how we're gonna do how we're going to get the centimeter cubed is by Putting all of this to power of three cubing it. All right. And of course if we want the sanctions to go ahead and cancel since we also cube the angstrom, we're gonna go ahead and also cube this. Alright, so putting that into my calculator of course are units of the angstrom will cancel leaving us with just the numerical value of 6.79 times 10 to the negative 23rd centimeter cute. Alright. Next calculation I'm going to do is to calculate the mass per unit cell. Okay, so how to do this? Is that we're gonna go ahead and take the density That's given to us. So 10.49 g per one centimeter. Cute. We're gonna take the volume of the unit cell that we just calculated for. Which is going to be 6.79 times 10 to the negative 23rd centimeter cubed for every one unit. So and as you can see our centimeter cubed will cancel giving us the numerical value of 7.12 times 10 to the negative 22. And the unit is going to be grams because grams on top here and my denominator unit will be Yoon itself. So that's going to be the mass per unit self. Alright. And lassie calculating the atomic mess. So I'm actually gonna scroll down just a little bit to give us a little bit more space. So now we're calculating for the atomic mass. Okay so starting off with the mass per unit. So they were given are not giving but we just calculated for above. That's 7.12 times 10 to the -22 g for every one unit. So so for every one unit there's going to be four atoms. And that's because of the problem we're given that it's a face centered cubic lattice. Okay, continuing on them, go ahead and use avocados number to convert our items into malls. So you know that is for everyone more. There are 6.02, 2 times 10 to the 23rd atoms. Alright so from this part we can see the units. Our council is the unit cell and the dreams Leaving us with a numerical value. Once I put all this into my calculator to be 107. minutes is g, her mole. And taking a look at my pirogue table. The element that matches closest to this mass, it's going to be silver. So it is horses too silver, which is the element symbol of a G. So our answer, The mass is going to be 107. grams per mole. And the element that we discovered this to be is silver with al maximo A. G. And this is going to be my final answer for this problem. Thank you all so much for watching.

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078 Å, and the density of the crystal is 19.30 g>cm3. Calculate the atomic weight of the element and identify the element.

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