# Ch 8 - Iowa State University

```Leader: Grant DeRocher
Course: Chem 167
Supplemental Instruction
Instructor: Houk
Iowa State University
Date: 03/05/13
Do a problem from end of ch 7 first as review. Then 8.10, 8.13, 8.17, 8.19,
Next Exam is Wed March 13
2 hour Exam Review on Sunday March 10, Room TBD
Ch 8
4. Polonium is the only metal that forms a simple cubic crystal structure. Use the fact that the
density of polonium is 9.32g/cm3 to calculate its atomic radius.
In the simple cubic crystal structure there are four Po atoms at the corners of each unit cell. The
lengths of a unit cell, a, equals two times its radius, a=2r. The number of Po atoms resent in the
simple cubic unit cell is 8*(1/8)=1 Po atom. The mass of one Po atoms is
1 πππ ππ
209 π ππ
:1 ππ ππ‘ππ π 6.022π₯1023 ππ‘πππ  ππ π 1 πππ ππ = 3.47π₯10−22 π. The volume of a unit cell is
Vcell=(a)3
Using density we can solve for the volume in terms of the cell edge length, a, and then finally
find a.
π=
d=m/v;
π
π
=
3.47π₯10−22 π
9.32 π/ππ3
= 3.72π₯10−23 ππ3 .
3
So π = √3.72π₯10−23 = 3.34π₯10−8 cm.
Now the cell edge a=2r so r=a/2 = 3.34x10-8/2= 1.67x10-8 cm
5. Europium forms a body-centered cubic unit cell and has density of 4.68g/cm3. From this
information, determine the length of the edge of a cubic cell.
The body centered cubic unit cell contains 8*(1/8) +1= 2 Eu atoms.
1 πππ πΈπ’
152.97 π πΈπ’
The mass of these two atoms is: 2 πΈπ’ ππ‘πππ  π 6.022π₯1023 ππ‘πππ  πΈπ’ π 1 πππ πΈπ’ = 5.080π₯10−22 π
The volume of this unit cell is Vcell= (a)3
Using density, we can solve for volume in terms of the cell edge length, a, and then finally find
a. d= m/V π =
So π =
π
=
5.080π₯10−22 π
= 1.09π₯10−22 ππ3
4.68 π/ππ3
3
√1.09π₯10−22 ππ3 = 4.78π₯10−8 ππ
π
```