Number of Atoms in Unit Cell — Prelims Questions

A metal crystallizes in a face-centered cubic (FCC) lattice. How many atoms are effectively present in one unit cell of this metal?

An element has a body-centered cubic (BCC) structure. If the atomic radius is $r$, what is the relationship between the edge length ($a$) of the unit cell and $r$?

An element (atomic mass $M$) crystallizes in a structure having 8 atoms at the corners and 1 atom at the body center of its unit cell. The density of the element is $ho$. If the edge length of the unit cell is $a$, what is the correct expression for Avogadro's number ($N_A$)?

Which of the following unit cells has the highest number of effective atoms (Z)?

An ionic compound forms a cubic unit cell where A ions are at the corners and B ions are at the face centers. What is the empirical formula of the compound?

A compound forms a hexagonal close-packed (HCP) structure. What is the effective number of atoms (Z) in its unit cell?