Answer:
1. [tex]a = 0.252nm[/tex]
[tex]a=2.52*10^{-8}cm[/tex]
2. [tex]V=0.016nm^{3}[/tex]
[tex]V=1.6*10^{-23}cc[/tex]
3. [tex]d=14.6\frac{g}{cc}[/tex]
Explanation:
1. Find the length of the unit cell:
a. In nanometers (nm):
[tex]a=2R[/tex]
[tex]a=2*0.126nm[/tex]
[tex]a=0.252nm[/tex]
b. Convert the radius from nm to cm to calculate the length of the unit cell In centimeters (cm):
[tex]0.126nm*\frac{1*10^{-7}cm}{1nm}=1.26^{-8}cm[/tex]
c. Apply the formula to find the lentht of the unit cell in cm:
[tex]a=2R[/tex]
[tex]a=2*(1.26*10^{-8})[/tex]
[tex]a=2.52*10^{-8}cm[/tex]
2. Find the volume of the unit cell:
[tex]V=a^{3}[/tex]
- In nanometers (nm):
[tex]V=(0.252nm)^{3}[/tex]
[tex]V=0.016nm^{3}[/tex]
- In cubic centimeters (cc):
[tex]V=(2.52*10^{-8}cm)^{3}[/tex]
[tex]V=1.6*10^{-23}cc[/tex]
3. Find the Density of the metal in grams per cubic centimeter:
[tex]d=\frac{(atoms/cell)*atomicweight}{unitcellvolume*Avogadrosnumber}[/tex]
[tex]d=\frac{(2\frac{atoms}{cell})*(70.4\frac{g}{mol})}{(1.6*10^{-23}cc)*(6.022*10^{23}\frac{atoms}{mol})}[/tex]
[tex]d=14.6\frac{g}{cc}[/tex]
