Answer:
Volume of face centered cubic cell=[tex]4.74531*10^{-29} m^3[/tex]
Explanation:
Consider the face centered cubic cell:
1 atom at each corner of cube.
1 atom at center of each face.
Consider the one face (ABCD) as shown in attachment for calculation:
Length of the all sides of face centered cubic cell is L.
Volume of face centered cubic cell= L^3
Now Consider the figure shown in attachment:
According to Pythagoras theorem on ΔADC.
[tex]L^{2}+L^2=(4a)^2[/tex] (a is the atomic radius)
[tex]L=\frac{4a}{\sqrt{2}}[/tex] (Put in the formula of Volume)
Volume of face centered cubic cell= L^3
Volume of face centered cubic cell= [tex](\frac{4a}{\sqrt{2}})^3[/tex]
Volume of face centered cubic cell= [tex](\frac{4(0.128*10^{-9}}{\sqrt{2}})^3[/tex]
Volume of face centered cubic cell=[tex]4.74531*10^{-29} m^3[/tex]
