Atomic packing factor of body centred cubic structure (bcc) is A. 0.63 B. 0.68 C. 0.69 D. 0.73

0.63
0.68
0.69
0.73

The correct answer is A. 0.63.

The atomic packing factor (APF) is a measure of how efficiently space is filled by atoms in a crystal structure. It is calculated by dividing the volume of the atoms in a unit cell by the volume of the unit cell.

The bcc structure has a unit cell that is a cube with an atom at each corner and an atom in the center of the cube. The volume of the atom is $\frac{4}{3}\pi r^3$, where $r$ is the radius of the atom. The volume of the unit cell is $a^3$, where $a$ is the length of the side of the cube.

The APF for the bcc structure is therefore:

$$APF = \frac{4}{3}\pi r^3 \times \frac{1}{a^3} = \frac{4}{3}\pi \left(\frac{r}{a}\right)^3$$

The radius of an atom is typically about 0.15 nm, and the length of the side of a bcc unit cell is typically about 0.5 nm. Substituting these values into the equation for the APF, we get:

$$APF = \frac{4}{3}\pi \left(\frac{0.15 \text{ nm}}{0.5 \text{ nm}}\right)^3 = 0.63$$

Therefore, the APF for the bcc structure is 0.63. This means that the atoms in a bcc crystal structure fill about 63% of the space in the crystal.

The other options are incorrect because they do not represent the actual APF of the bcc structure.