Question

Copper has face-centered cubic (FCC) lattice with interatomic spacing equal to 2.54. The value of lattice constant for this lattice is:
A. 3.59 A
B. 2.54 A
C. 1.27 A
D. 5.08 A.

Answer 1

Hint: FCC means face centered cubic packing. FCC (face-centered cubic) has six faces and eight corners. There is a formula to calculate lattice constants by using interatomic space and it is as follows.
Lattice constant for FCC = interspacing capacity $\times \sqrt{2}$

Complete step by step answer:
- In the question it is given that copper has FCC (face-centered cubic) lattice with interatomic spacing equal to 2.54.
- We have to calculate the lattice constant by using the given data.
- The lattice constant for FCC (face-centered cubic) can be calculated as follows.
Lattice constant for FCC (face-centered cubic) = interspacing capacity $\times \sqrt{2}$
Interspacing capacity or interatomic space = 2.54
- Substitute all the known values in the above formula to get the lattice constant for FCC (face-centered cubic).
 Lattice constant for FCC = interspacing capacity $\times \sqrt{2}$
Lattice constant for FCC = 2.54 $\times \sqrt{2}$ = 3.59 A.
- Therefore the value of lattice constant for copper is 3.59 A.
So, the correct answer is “Option A”.

Note: The unit for lattice constant is angstrom. Interatomic space for Face centered cubic lattice is 2r. Means interatomic space is equal to two times the radius of the FCC lattice. The relationship can be written in the form of formula and it is as follows.
Interatomic space = 2r
Here r = radius of the atom