Suppose the radius of an atom in a body-centered cubic unit...

Suppose the radius of an atom in a body-centered cubic unit cell is 0.29 nm. What is the edge length of the unit cell in nm. Answer: Hypothetical metal M has a molecular weight 177 g/mol and crystallizes in a body-centered cubic array of atoms in which the length of the unit cell's edge is 393.5 pm (10-12 m). Calculate the density of the metal in g/cm3. Answer:

Transcript

00:01 For a body centered cubic, we have eight spheres, one at each edge, or one at each point of the cube.

00:16 And then we have one right in the middle, which i'll make a different color.

00:24 And this edge length, in terms of the radius of an atom, is going to be four times r, divided by the square root of three.

00:44 I don't know whether it wanted you to figure that out or they've given you that equation or what, but it just comes from the geometry where r is equal to the radius of a sphere comprising the body -centered cubic arrangement.

01:08 So it'll be four times r, which is provided.

01:14 Suppose the radius of an atom in a body -centered cubic unit cell is point.

01:19 To 9 nanometers.

01:22 And we divide that by the square root of 3.

01:28 And we get to just two significant figures, because that's all we have with the radius.

01:36 0 .67 nanometers.

01:42 Then to determine the density, we need to know the number of atom equivalents that are found in the unit cell.

01:48 We've got one -eighth of an atom at all eight corners, so that's a total of one and one right in the middle.

01:57 So n equals two.

01:59 We've got two atom equivalents per unit cell.

02:06 So knowing the length of the edge of a unit cell is 393 .5 picometers, we can calculate the density in grams per centimeter.

02:21 Okay, so to do this, density is going to be equal to mass...

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