Question

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

Answer 1

Volume of face centered cubic cell=
`4.74531*10^(-29) m^3`

Step-by-step 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=(4a)/(√(2))` (Put in the formula of Volume)

Volume of face centered cubic cell= L^3

Volume of face centered cubic cell=
`((4a)/(√(2)))^3`

Volume of face centered cubic cell=
`((4(0.128*10^(-9))/(√(2)))^3`

Volume of face centered cubic cell=
`4.74531*10^(-29) m^3`