Question:

A solid $AB$ has $NaCl$ type structure. The radius of $A^+$ is $100\, pm$. What is the radius of $B^-$ ?

Updated On: Jul 14, 2022
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The Correct Option is A

Solution and Explanation

$NaCl$ type structure is also called face centred cubic lattice. Here the radius ratio $(r_c /r_a )$ ranges from $0.414$ to $0.732$. Radius ratio $= \frac{r_{c}}{r_{a}} = \frac{\text{radius of cation}}{\text{radius of anion}}$ $\Rightarrow$ Radius of anion $\left(B^{-}\right)= \frac{\text{radius of } A^{+}}{\text{radius ratio}}$ $= \frac{100}{0.414}$ to $\frac{100}{0.732}$ $= 241.5$ to $136.6.$
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Concepts Used:

Solid State

Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions. 

Solid State

Types of Solids:

Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;

  • Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
  • Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.