[amp_mcq option1=”0.63″ option2=”0.68″ option3=”0.69″ option4=”0.73″ correct=”option1″]<\/p>\n
The correct answer is A. 0.63.<\/p>\n
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.<\/p>\n
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.<\/p>\n
The APF for the bcc structure is therefore:<\/p>\n
$$APF = \\frac{4}{3}\\pi r^3 \\times \\frac{1}{a^3} = \\frac{4}{3}\\pi \\left(\\frac{r}{a}\\right)^3$$<\/p>\n
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:<\/p>\n
$$APF = \\frac{4}{3}\\pi \\left(\\frac{0.15 \\text{ nm}}{0.5 \\text{ nm}}\\right)^3 = 0.63$$<\/p>\n
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.<\/p>\n
The other options are incorrect because they do not represent the actual APF of the bcc structure.<\/p>\n","protected":false},"excerpt":{"rendered":"
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