Question

A solid compound XY has $\text{NaCl}$ structure. If the radius of the cation is 100 pm, the radius of the anion $\text{(}{{\text{Y}}^{-}})$ will be:
A. 275.1 pm
B. 322.5 pm
C. 241.5 pm
D. 165.7 pm.

Answer 1

Hint: The division of the radius of cation by the radius of anion gives the radius ratio. It is very helpful in telling the structure of the compound by using the coordination number i.e. more will be the coordination number more is the radius of an ion or atom.

Formula used:

Complete step by step answer:
- In the structure of sodium chloride, the chlorine ion i.e. anion is present in the CCP or Cubic Close Packing whereas the cation or sodium ion is present in all the octahedral voids.
- CCP or cubic close packing is the crystal structure in which the arrangement of spheres is done in such a way that it forms octahedral voids and the packing is known as ABCABC type. It has three layers of the spheres.
- We all know the octahedral voids are formed when two triangular voids of second and first layer join then the interstitial void formed is known as octahedral void.
- So, according to this, the sodium and chlorine both have a coordination number 6 because one sodium atom connects with six chlorine atoms and one chlorine connects with six sodium atoms.
- Now, according to the given values of the radius ratio with their coordination number, the radius ratio of NaCl should be 0.414.
- So, $0.414\text{ = }\frac{\text{Radius of cation (}{{\text{r}}^{-}})}{\text{Radius of anion (}{{\text{r}}^{+}})}$
- It is given that the radius of the cation is 100 pm so we can calculate the radius of anion by using the above formula and we will get:
$0.414\text{ = }\frac{100}{\text{r}}$ 
$\text{r = }\frac{100}{0.414}\text{ = 241}\text{.5 pm}$
The radius ratio of sodium chloride is 241.5 pm which means it has an octahedral void.
Therefore, option C is the correct answer.
Note: The radius ratio is different for different coordination numbers such as for coordination no. 2 the radius ratio will be less than 0.155 and have linear void whereas highest coordination no. 8 has the radius ratio of 0.732 to 1.000 which have a cubic void.