If the total volume of a simple cubic unit cell is 6.817 × 10-23 cm3, what is the volume occupied by particles in the unit cell?
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In a simple cubic unit cell, the volume occupied by the particles is equivalent to the volume of the unit cell. For other structures, account for the number of particles per unit cell.
In a simple cubic unit cell, each corner possesses one particle; however, each corner particle is shared by eight adjacent unit cells. Consequently, the net quantity of particles within a simple cubic unit cell amounts to 1 (calculated as 8 corner particles × 1/8 contribution per unit cell).
The volume occupied by particles within the unit cell signifies the space actualized by the particles, excluding any void areas. For a simple cubic unit cell, this volume represents the effective space taken up by the particles.
The proportion of the unit cell's volume occupied by particles (termed packing efficiency) in a simple cubic arrangement is relatively low, approximately 52.4%. This is due to a less dense packing configuration compared to structures such as face-centered cubic or body-centered cubic.
The volume occupied by particles is determined by multiplying the total unit cell volume by its packing efficiency.
Calculation:
Total unit cell volume = 6.817 × 10-23 cm3
Packing efficiency for simple cubic = 52.4% = 0.524
Volume occupied by particles = Total volume × Packing efficiency
Volume occupied by particles = (6.817 × 10-23) × 0.524
Result: The volume occupied by particles within the unit cell is approximately 3.57 × 10-23 cm3.