Question

Copper has face centered cubic (fcc) lattice with interatomic spacing equal to 2.54 Å. The value of lattice constant for this lattice is(a) 2.54 Å(b) 3.59 Å(c) 1.27 Å(d) 5.08 Å

Answer 1

answer : option (b) 3.59 Å

explanation : use formula,

lattice constant for fcc = interatomic space × $\sqrt{2}$

it is given that, interatomic space = 2.54 Å

so, lattice constant for fcc = 2.54 Å × √2

= 2.54 × 1.414 Å

= 3.59156 Å

≈ 3.59 Å

hence, The value of lattice constant for this lattice is 3.59 Å

Answer 2

FCC  stands for Face-centered cubic lattice.It has lattice points at the eight corners of the unit cell including ancillary points at the centres of each face of the unit cell. It includes unit cell vectors a =b =c and inter-axial angles α=β=γ=90°.

The solution for the question is : B

The inter-atomic spacing for a fcc lattice  

r  ≈  [(a2)²+(a2)²+(0)²]1/2   ≈ a÷2√            

a being lattice constant.                        

Interatomic spacing is  precisely the nearest neighbours distance.