Question

If the atomic radius of copper is 0.128 nm, calculate the volume of its unit cell in cubic meters.

Answer 1

Answer:

Volume of face centered cubic cell=$4.74531*10^{-29} m^3$

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.

$L^{2}+L^2=(4a)^2$     (a is the atomic radius)

$L=\frac{4a}{\sqrt{2}}$ (Put in the formula of Volume)

Volume of face centered cubic cell= L^3

Volume of face centered cubic cell= $(\frac{4a}{\sqrt{2}})^3$

Volume of face centered cubic cell= $(\frac{4(0.128*10^{-9}}{\sqrt{2}})^3$

Volume of face centered cubic cell=$4.74531*10^{-29} m^3$