Atomic packing factor (APF) for SC. 0.52.a O 0.74.b O 0.68.c O 0.93.d O
The Correct Answer and Explanation is:
The correct answer for the atomic packing factor (APF) of Simple Cubic (SC) is 0.52 (a).
Explanation:
The Atomic Packing Factor (APF) is a measure of how efficiently the atoms are packed into a structure. It is calculated as the ratio of the volume occupied by atoms in the unit cell to the total volume of the unit cell.
In a simple cubic (SC) structure:
- Each unit cell has 1 atom.
- The atoms touch each other along the edges of the unit cell.
- The atoms are positioned at the corners of the cube.
To calculate the APF for SC:
- The volume of the unit cell is a3a^3a3, where “a” is the edge length of the unit cell.
- The number of atoms per unit cell is 1.
- The volume occupied by each atom is the volume of a sphere with radius rrr, and the formula for the volume of a sphere is 43πr3\frac{4}{3} \pi r^334πr3.
- In an SC structure, the edge length aaa is equal to 2 times the atomic radius rrr, i.e., a=2ra = 2ra=2r.
Thus, the APF for SC is calculated as:APF=Volume occupied by atoms in the unit cellTotal volume of the unit cell=43πr3a3=43πr3(2r)3=16π≈0.52APF = \frac{\text{Volume occupied by atoms in the unit cell}}{\text{Total volume of the unit cell}} = \frac{\frac{4}{3} \pi r^3}{a^3} = \frac{\frac{4}{3} \pi r^3}{(2r)^3} = \frac{1}{6} \pi \approx 0.52APF=Total volume of the unit cellVolume occupied by atoms in the unit cell=a334πr3=(2r)334πr3=61π≈0.52
Therefore, the correct APF for Simple Cubic (SC) is 0.52.
