Question

If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.137 nm, calculate the volume of its unit cell.

Answer 1

`5.796* 10^(-29)m^3`

Explanation:

Atomic radius of metal=0.137nm=
`0.137* 10^(-9)`m

`1nm=10^(-9)m`

Structure is FCC

We know that

The relation between edge length and radius in FCC structure

`a=2\sqrt 2r`

Where a=Edge length=Side

r=Radius

Using the relation

`a=2\sqrt 2* 0.137* 10^(-9)=0.387* 10^(-9)m`

We know that

Volume of cube=
`(side)^3`

Using the formula

Volume of unit cell=
`(0.387* 10^(-9))^3=5.796* 10^(-29) m^3`