Question

In NaCl crystal, the radius ratio is :
A ) 0.4
B ) 0.98
C ) 1.0
D ) 0.52

Answer 1

Radius ratio is the ratio of radius of cation to the ratio of the radius of anion. Usually cation is smaller than anion. Hence, the radius ratio is less than one.

Complete answer:
In an ionic crystal lattice, the radius ratio is used to predict the coordination number of the ion and the arrangement of ions in the crystal lattice.

Radius ratio	Coordination number	Geometry of holes (voids)
0.155-0.225	3	Trigonal planar
0.225-0.414	4	tetrahedral
0.414-0.732	6	octahedral
0.732-1.00	8	cubic

Sodium chloride crystal has face centered cubic arrangement of chloride ions. Sodium ions are present in octahedral voids. Each sodium ion is surrounded by six chloride ions. Each chloride ion is surrounded by six sodium ions. So the coordination number for sodium cation is six. Similarly the coordination number for chloride anion is six.
According to the radius ratio rule, the coordination number of six corresponds to the radius ratio of 0.414-0.732. Of the given options, the value 0.52 is in the range 0.414-732.
Hence, sodium chloride crystal has the radius ratio of 0.52.

Hence, the option D ) is the correct answer.

Note: If the radii of cation and anion are given then it is possible to determine the arrangement of ions in the crystal, the coordination number of cation and anions and the geometry of holes (voids). For each geometry of voids (tetrahedral, octahedral etc), there is a range of radius ratios. Thus, if the radius ratio of an ionic compound is in the range 0.414-0.732, then the geometry of voids is octahedral.