An element atomic mass 192 having face centered cubic...

An element (atomic mass = 192) having face-centered cubic crystal has a density of 22.56 g/cm3. Find the distance (in nanometers, up to 2 decimal figures) between the center of one corner atom and the center of the atom located in the middle of the side of the unit cell. Clue: You need the value of the edge length to solve for the required quantity.

Transcript

00:01 So for the fist -centered cubic, the density equals to the mass of the atoms in a cubic, so the volume of the cube.

00:22 So let's see you have four atom because that is the total number of atoms in the fifth -centered the cube.

00:37 Then you multiply the molar mass, which is one 90 gram per more.

00:47 So that, and then you divided by the avocado's number, so that it will give you the mass of four atoms in a cube.

01:08 So then that is the mass.

01:10 Now you look at the volume.

01:12 Remember that if the radius of the is r, then the cell is square root of 8 multiply r.

01:27 Of course, that should be the cubic.

01:32 But i'm going to try to, because right here, the r is not defined.

01:38 What's the unit? so what if we wanted to do is trying to see that we assume that the unit right here is nanometer.

01:45 If you need to write here as nanometer, i want to convert the nanometer.

01:54 I want to convert the nanometer eventually to a centimeter cubic centimeter, so that on both sides would be the same.

02:07 So first i convert it to the meter, then i convert a meter to the centimeter.

02:18 So that i take power of 3.

02:23 So that will be the total volume.

02:27 Remember, i assume right here, r is a nanometer.

02:33 So now i can finish all these calculations.

02:41 So i'm going to get rid of all the unit, okay? the unit will be canceled...

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