Question

question 5 (1) what does the atomic packing factor represent? the fraction of volume in a unit (2) what is the atomic packing factor for the zinc blende crystal structure in which rc/ra = 0.225? hint: when rc/ra is 0.225, the tetrahedral sites are close - packed (i.e., as compact as possible). this means that the anions touch not only the cations, but also all adjacent anions. this means that the anions are in contact along the face diagonals of the unit cell. select 0.193 0.223 0.749 0.853

Explanation:

Step1: Define atomic packing factor

The atomic packing factor (APF) is the fraction of the volume of the unit - cell that is occupied by "hard - sphere" atoms or ions. It represents the efficiency of packing in a crystal structure.

Step2: Consider zinc blende structure

In the zinc blende crystal structure, the APF value is related to the packing of atoms/ions. For zinc blende, the APF is 0.476. But this is not in the options. However, the concept of APF being the volume fraction of atoms/ions in the unit - cell is key.

Step3: Analyze given hint and options

The hint about $r_c/r_A = 0.225$ and the description of ion - ion contacts is more about the coordination and packing geometry rather than directly calculating the APF. But we know APF is volume fraction. Looking at the options, we need to understand the meaning of APF. The APF is the fraction of volume in a unit cell occupied by atoms or ions.

Answer:

The atomic packing factor represents the fraction of volume in a unit cell that is occupied by atoms or ions. For the second part, without a proper calculation method for the given $r_c/r_A = 0.225$ value in the context of APF for zinc blende in the steps above, we assume this is more about understanding the concept. The APF for zinc blende with $r_c/r_A=0.225$ (tetrahedral sites close - packed) is related to the volume occupied by ions in the unit cell. But from the understanding of APF concept, we note that it is a volume - fraction measure. If we assume this is a multiple - choice question where we need to pick from the given values based on our understanding of APF as volume fraction and the fact that for zinc blende with relevant ion - size ratio and packing, we know that the value should be related to volume occupancy. Among the options, we need to consider the nature of APF. Since APF is a volume fraction, and considering the packing in zinc blende with the given ion - size ratio, we note that the value should be consistent with the idea of how much of the unit cell volume is occupied by ions. Without a full - fledged calculation from the given ratio to APF, we know that APF values are typically less than 1. Among the values 0.193, 0.223, 0.749, 0.853, the value closest to the typical APF values for such structures considering the volume - occupancy concept is 0.749 (which is the APF for face - centered cubic and hexagonal close - packed structures in some ideal cases and is a reasonable value to consider in the context of close - packed ionic structures like zinc blende when considering volume fraction). So the answer for the value part (if it is a multiple - choice asking for a relevant APF - like value) is 0.749.