00:05
We are told that lead, which is used in solder and as a radiation shield, adopts a face -centered cubic structure.
00:13
Each atom has a diameter of 0 .35 nanometers.
00:17
We are asked to find the theoretical density of lead if molar mass is 207 .2.
00:30
Make sure i got a nice point there, grams per wall.
00:35
So for face -centered cubic, n is equal to four.
00:44
There's four parts of the unit cell.
00:48
My radius will equal 0 .35 nanometers divided by 2, which will be 0 .35 times 10 to the minus 9th, divided by 2.
01:08
I guess i want to go 7th.
01:14
Here, i'll set it up so you can see what i'm doing.
01:16
0 .35 nanometers divided by 2.
01:23
And i want to convert this to centimeters because i want centimeters cubed in a moment.
01:37
Let me get my calculator.
01:39
I think it's going to be 3 .5 times 10 to the 8th, but let me do it.
01:51
3 .5 times 10 to the minus 8th.
01:59
Okay, so we know that 4 times our edge length, and you can just look this up for which one you need to do.
02:11
You can go through the whole process of drying your cubes and figuring it out if you want.
02:16
But it's going to be a, our edge length is going to be four times r divided by the square root of two.
02:30
Let me do that.
02:35
Four times three point five times ten to the minus eighth divided by the square root of two.
02:44
Enter.
02:59
And then our density, i'll switch colors, will equal n times a times six, divided by avagadro's number and divided by area cubed.
03:37
And this is the molar mass...