[amp_mcq option1=”0.63″ option2=”0.68″ option3=”0.69″ option4=”0.73″ correct=”option1″]
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.