Question

Given below are statements
Statement I: Unit cell in a lattice has six characteristic parameters
Statement II: In fcc lattice, the total number of atoms/ions per unit cell is 4

• A. Both Statements I and II are correct
• B. Both Statements I and II are not correct
• C. Statement I is correct but statement II is not correct
• D. Statement I is not correct but statement II is correct

Hint:

For cubic unit cells:
Simple cubic (sc) has $Z = 1$.
Body-centered cubic (bcc) has $Z = 2$.
Face-centered cubic (fcc) has $Z = 4$.

Answer 1

The Correct Option is A

Step 1: Check statement I.
A unit cell is fully described by three edge lengths, $a, b, c$, and the three angles between them, $\alpha, \beta, \gamma$, six parameters in total, so this statement is correct.
Step 2: Check statement II by counting atoms in an fcc cell.
An fcc cell has 8 corner atoms contributing $8 \times \tfrac{1}{8} = 1$, and 6 face atoms contributing $6 \times \tfrac{1}{2} = 3$, giving a total of $1+3=4$ atoms per unit cell.
Step 3: Combine both checks.
Both statements survive independent verification.
Final answer: Option 1, both statement I and statement II are correct.