A solid AB has NaCl type structure with edge length 580.4pm . The radius of ${A^ + }$ is 100pm . What is the radius (in pm) of ${B^ - }$?
A.190.20
B.540.13
C.525.23
D.78.12

Hint: Sodium chloride is an ionic compound in which sodium and chloride ions are in the ratio of $1:1$.The crystal structure is an ordered array of atoms, ions, or molecules. In the case of NaCl structure, each atom has six nearest neighbors, with octahedral geometry. This arrangement is known as cubic close packing.
Formula used:
${r_c} + {r_a} = \dfrac{a}{2}$
Where, ${r_c} = $radius of cation, ${r_a} = $radius of anion and a$ = $edge length

Complete step by step answer:
Crystal structure is obtained by attaching atoms, groups of atoms or molecules. This structure occurs from the intrinsic nature of the constituent particles to produce symmetric patterns.
NaCl has a cubic unit cell. It is best thought of as a face centered cubic array of anions with an interpreting fcc cation lattice (or vice versa). Its structure is as shown:

Now, in the given question, the edge length is 580.4pm and the radius of cation is 100pm. Let’s find out the radius of anion.
As we know that $NaCl$ has fcc structure, thus according to the formula,
${r_c} + {r_a} = \dfrac{a}{2}$
$100 + {r_a} = \dfrac{{580.4}}{2}$
$ = 290.2pm$
Now, $100 + {r_a} = 290.2pm$
Therefore, ${r_a} = 290.2 - 100$
$ = 190.2pm$

Hence, option A is correct.

Note:
In its aqueous state, NaCl acts as a good conductor of electricity due to the free movement of the ions. It is easily soluble in water and partially soluble in other liquids. It is a major raw material in the industrial manufacturing of various chemicals such as sodium carbonate, sodium hydrogen carbonate etc.