An element X which crystallises in face centred cubic structure. Its metallic radius is 145 pm, the length of the side of the unit cell is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 410.1 pm
In a face-centred cubic unit cell the atoms touch along the face diagonal. The face diagonal = √2 a = 4r, so
a = 4r/√2 = 2√2 r
a = 2 × 1.414 × 145 pm = 410.1 pm
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic is not there in the latest NCERT book (2026-27), and it is also out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Packing Efficiency in hcp and ccp Structures – “… Let us calculate the efficiency of packing in ccp structure. In Fig. 1.20 let the unit cell edge length be ‘a’ and face diagonal AC = b. In ΔABC, AC2 = b2 = BC2 + AB2 = a2 + a2 = 2a2 or b = √2 a. If r is the radius of the sphere, we find b = 4r = √2 a or a = 4r/√2 = 2√2 r”
