Question

Identify the edge lengths \((a,b,c)\) in the unit cell shown below.

• A. \(i=a,\;j=b,\;k=c\)
• B. \(i=a,\;j=c,\;k=b\)
• C. \(i=c,\;j=b,\;k=a\)
• D. \(i=b,\;j=c,\;k=a\)

Hint:

In unit cell diagrams, three mutually perpendicular edges from one corner represent lattice parameters \(a,b,c\).

Answer 1

The Correct Option is A

Concept: In solid state chemistry, a unit cell represents the smallest repeating structural unit of a crystal lattice. Every unit cell is characterized by three edge lengths: \[ a,\qquad b,\qquad c \] and three interaxial angles: \[ \alpha,\qquad \beta,\qquad \gamma \] The edge lengths correspond to the three mutually intersecting edges originating from a single corner of the unit cell.

Step 1: Understand unit cell geometry carefully. The three dimensions of a crystal lattice are measured along three principal axes. Conventionally: \[ a=\text{x-axis length} \] \[ b=\text{y-axis length} \] \[ c=\text{z-axis length} \]

Step 2: Interpret labels given in diagram. The question diagram labels three edges as \[ i,\qquad j,\qquad k \] These correspond to the three crystallographic axes. Standard crystallographic notation assigns: \[ i\rightarrow a \] \[ j\rightarrow b \] \[ k\rightarrow c \]

Step 3: Compare with options. Only option A matches correct crystallographic assignment. Thus answer becomes \[ \boxed{i=a,\qquad j=b,\qquad k=c} \]