Question

Which of the following statement(s) is/are true about the hexagonal close packing in 3-D?

• A. Third layer is covering the octahedral voids of second layer
• B. First layer is identical to the third layer
• C. Second layer occupies 50% of the voids of first layer
• D. Spheres of the fourth layer are exactly aligned with those of the first layers arrangement,

Answer 1

Answer: (B), (C)

Second layer occupies 50% of the voids of first layer

3-D hexagonal close packing is formed from 2-D hexagonal closed packing. Here, the second row of spheres is placed in the interstices or depressions of the first-row spheres of 2-D hexagonal close packing. Only 50% void of one layer can be occupied by sphere of other layer (II layer).
Spheres of third layer are placed over second layer covering the
tetrahedral voids so that, spheres of third layer are exactly aligned with the spheres of first layer
This leads to arrangement of ABABAB... pattern. This structure is called hexagonal close packing (hcp) structure. Packing in Mg, Zn, Cd etc. follows this type of arrangement.
This can be diagrammatically represented as


Here, we can see easily that $1^{st}$ layer and $4^{th}$ layer are not exactly aligned.
Thus, statement (d) is not correct

Hence, statement (b) and (c) are correct.