In the density formula ρ = (sum_i N_i M_i) / (N_A V_cell), what does V_cell represent?

• A. Volume of the entire crystal
• B. Unit cell volume
• C. Volume per atom
• D. Avogadro's volume

Answer: (B)

This uses the unit cell as the volume reference. V_cell represents the volume of the unit cell, the smallest repeating box that tessellates the crystal. The density is mass per unit volume, so the numerator sums the mass inside one unit cell: for each species, you multiply how many atoms are in the cell (N_i) by its molar mass (M_i) and divide by Avogadro’s number to convert to grams, then add over all species. Dividing that total mass by V_cell gives the mass per unit volume. So V_cell is specifically the volume of the unit cell, not the entire crystal, not volume per atom, and not Avogadro’s volume.