Question
An element with a molar mass 27g mol^ -1 forms a cubic unit cell. Calculate the number of atoms present in a unit cell if the density of metal is 2.7g cm^ -3 . [a^3 N_A = 40 cm^3 mol^ -1 ]
MHT CET
Chemistry
Solid State
2026
MHT CET 2026 (13 April Shift 1)
MHT CET Chemistry Question (2026) — Solution
Options
- A. 1
- B. 2
- C. 4
- D. 6
Answer
C. 4
Step-by-step solution
The density of a cubic unit cell is given by the formula: d = Z M a^3 N_A where Z is the number of atoms per unit cell, M is the molar mass, a is the edge length, and N_A is Avogadro's number. Rearranging the formula to solve for Z: Z = d (a^3 N_A) M Substituting the given values d = 2.7 g cm^ -3 , M = 27 g mol^ -1 , and a^3 N_A = 40 cm^3 mol^ -1 : Z = 2.7 40 27 Z = 108 27 = 4 The number of atoms present in the unit cell is 4.
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