Question

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?

• A. 3.57 $\times$ 10$^{-23}$ cm$^3$
• B. 4.57 $\times$ 10$^{-23}$ cm$^3$
• C. 5.57 $\times$ 10$^{-23}$ cm$^3$
• D. 6.57 $\times$ 10$^{-23}$ cm$^3$

Hint:

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.

Answer 1

The Correct Option is A

• In a simple cubic unit cell, each corner of the cube has one particle (such as an atom or ion), but each corner atom is shared by eight neighboring unit cells. Therefore, the effective number of particles per unit cell in a simple cubic structure is 1 (since 8 corner atoms × 1/8 per unit cell = 1 particle per unit cell).
• The volume occupied by particles in the unit cell refers to the volume taken up by the actual particles, not the empty space within the cell. In the case of a simple cubic unit cell, the volume occupied by the particles is the effective volume of the unit cell that is occupied by the particles.
• In a simple cubic unit cell, the fraction of the unit cell volume occupied by particles (also called the packing efficiency) is relatively low. It is approximately 52.4% because the atoms are arranged in a less efficient packing compared to other structures like face-centered cubic or body-centered cubic.
• To calculate the volume occupied by particles, we multiply the total volume of the unit cell by the packing efficiency.

Calculation:

• Total volume of the unit cell = 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 in the unit cell is approximately 3.57 × 10^-23 cm³.