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
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
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
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For cubic unit cells:
Simple cubic (sc) has $Z = 1$.
Body-centered cubic (bcc) has $Z = 2$.
Face-centered cubic (fcc) has $Z = 4$.
Simple cubic (sc) has $Z = 1$.
Body-centered cubic (bcc) has $Z = 2$.
Face-centered cubic (fcc) has $Z = 4$.
Updated On: Jul 22, 2026
- Both Statements I and II are correct
- Both Statements I and II are not correct
- Statement I is correct but statement II is not correct
- Statement I is not correct but statement II is correct
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
This question is a statement-based problem about solid-state chemistry.
We need to evaluate the accuracy of statements regarding unit cell parameters and face-centered cubic (fcc) lattices.
Step 2: Key Formula or Approach:
A unit cell is characterized by its dimensions along its three edges ($a, b, c$) and the angles between these edges ($\alpha, \beta, \gamma$).
The total number of atoms per unit cell in any cubic lattice is calculated as:
\[ Z = N_{\text{corner}} \times \left(\frac{1}{8}\right) + N_{\text{face}} \times \left(\frac{1}{2}\right) + N_{\text{body}} \times (1) + N_{\text{edge}} \times \left(\frac{1}{4}\right) \]
Step 3: Detailed Explanation:
• Statement I: "Unit cell in a lattice has six characteristic parameters."
This statement is correct. A unit cell is geometrically defined by 6 lattice parameters:
Three edge lengths: $a, b,$ and $c$.
Three axial angles: $\alpha$ (between $b$ and $c$), $\beta$ (between $a$ and $c$), and $\gamma$ (between $a$ and $b$).
• Statement II: "In fcc lattice, the total number of atoms/ions per unit cell is 4."
This statement is correct. In a face-centered cubic (fcc) lattice:
Atoms are located at all 8 corners of the cube, and each corner atom is shared among 8 adjacent unit cells.
Atoms are also located at all 6 face centers of the cube, and each face-centered atom is shared between 2 adjacent unit cells.
The total number of atoms per unit cell ($Z$) is:
\[ Z = 8 \times \left( \frac{1}{8} \right) + 6 \times \left( \frac{1}{2} \right) = 1 + 3 = 4 \]
• Since both statements are correct, the correct option is (A).
Step 4: Final Answer:
Both Statement I and Statement II are correct.
This question is a statement-based problem about solid-state chemistry.
We need to evaluate the accuracy of statements regarding unit cell parameters and face-centered cubic (fcc) lattices.
Step 2: Key Formula or Approach:
A unit cell is characterized by its dimensions along its three edges ($a, b, c$) and the angles between these edges ($\alpha, \beta, \gamma$).
The total number of atoms per unit cell in any cubic lattice is calculated as:
\[ Z = N_{\text{corner}} \times \left(\frac{1}{8}\right) + N_{\text{face}} \times \left(\frac{1}{2}\right) + N_{\text{body}} \times (1) + N_{\text{edge}} \times \left(\frac{1}{4}\right) \]
Step 3: Detailed Explanation:
• Statement I: "Unit cell in a lattice has six characteristic parameters."
This statement is correct. A unit cell is geometrically defined by 6 lattice parameters:
Three edge lengths: $a, b,$ and $c$.
Three axial angles: $\alpha$ (between $b$ and $c$), $\beta$ (between $a$ and $c$), and $\gamma$ (between $a$ and $b$).
• Statement II: "In fcc lattice, the total number of atoms/ions per unit cell is 4."
This statement is correct. In a face-centered cubic (fcc) lattice:
Atoms are located at all 8 corners of the cube, and each corner atom is shared among 8 adjacent unit cells.
Atoms are also located at all 6 face centers of the cube, and each face-centered atom is shared between 2 adjacent unit cells.
The total number of atoms per unit cell ($Z$) is:
\[ Z = 8 \times \left( \frac{1}{8} \right) + 6 \times \left( \frac{1}{2} \right) = 1 + 3 = 4 \]
• Since both statements are correct, the correct option is (A).
Step 4: Final Answer:
Both Statement I and Statement II are correct.
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