
Concept explainers
Consider the three types of cubic units cells.
- (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube’s edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)πr3, where r is the radius of the sphere.)
- (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?
(a)

Interpretation:
Percentage of occupied space within the unit cell has to be calculated.
Concept introduction:
Answer to Problem 46GQ
Percentage of occupied space within the unit cell is given below
More dense is FCC and least dense is simple primitive
Explanation of Solution
Calculate the packing efficiency of primitive cell
Calculate the packing efficiency of FCC
One unit cell of the fcc contains four atoms therefore,
Calculate the packing efficiency of BCC
By comparing packing efficiency percentage of the above three unit cell more the percentage, more the dense, therefore,
More dense is FCC and least dense is simple primitive
(b)

Interpretation:
On comparing the percentage of occupied space in PC with BCC and FCC, most dense and least dense has to be identified.
Concept introduction:
Answer to Problem 46GQ
More dense is FCC and least dense is simple primitive
Explanation of Solution
Percentage of occupied space within the unit cell is given below
By comparing packing efficiency percentage of the above three unit cell more the percentage, more the dense, therefore,
More dense is FCC and least dense is simple primitive
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