Q.12 Potassium metal crystallizes in the body-centered cubic structure. The number of atoms per unit cell is equal to
- (A) one
- (B) two
- (C) three
- (D) four
Potassium metal’s body-centered cubic (BCC) structure contains 2 atoms per unit cell. The correct answer is (B) two.
Option Analysis
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(A) one: This applies to primitive cubic or simple cubic structures, where only 8 corner atoms contribute (each shared by 8 cells: 8 × 1/8 = 1 atom total). BCC has an extra central atom, so this is incorrect.
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(B) two: In BCC, 8 corner atoms contribute 1 atom (8 × 1/8 = 1), plus 1 fully enclosed body-center atom, totaling 2 atoms. This matches potassium’s lattice.
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(C) three: No standard cubic structure yields exactly 3 atoms; this might confuse BCC contributions but ignores proper sharing rules.
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(D) four: This fits face-centered cubic (FCC) structures (8 corners × 1/8 + 6 faces × 1/2 = 4 atoms), not BCC.
Potassium metal adopts a body-centered cubic structure, a common crystal lattice in metals where atomic packing determines key properties like density. Understanding the number of atoms per unit cell in this body-centered cubic structure is essential for students tackling solid-state chemistry in exams like JEE or NEET.
BCC Structure Basics
A body-centered cubic unit cell features atoms at all 8 corners and one at the cube’s center. Corner atoms share across 8 adjacent cells, contributing 1/8 each (8 × 1/8 = 1 atom). The central atom belongs entirely to the cell (1 atom), yielding 2 atoms total in the body-centered cubic structure.
Why Potassium Fits BCC
Potassium, an alkali metal, crystallizes in BCC due to its large atomic radius and low density needs. This confirms 2 atoms per unit cell, as verified in multiple educational resources analyzing its lattice.
Comparison Table
Lattice Type Corner Contribution Face/Body Contribution Total Atoms per Unit Cell Primitive Cubic 8 × 1/8 = 1 None 1 Body-Centered Cubic (BCC) 8 × 1/8 = 1 1 (center) 2 Face-Centered Cubic (FCC) 8 × 1/8 = 1 6 × 1/2 = 3 4 -
