The compound producing Schottky defect, when added to crystals \(AgCl\) are:

A. \(NaCl\)

B. \(CdCl_2\)

C. \(CaCl_2\)

D. \(KCl\)

Choose the correct answer from the options given below:

B and C only

The correct answer is option 3. B and C only.

A Schottky defect is a type of point defect in crystals where equal numbers of cations and anions are missing from their lattice sites. This creates vacancies and disrupts the overall stoichiometry of the crystal.

Factors Affecting Schottky Defects:

The likelihood of a compound introducing Schottky defects into \(AgCl\) crystals depends on two main factors:

Ionic Size Ratio: When the sizes of the cation and anion in the added compound are similar to those in \(AgCl\) (\(Ag^+\) and \(Cl^-\)), it's easier for them to substitute for each other in the lattice and create vacancies.

Charge Balance: To maintain electrical neutrality, the added compound must introduce equal numbers of missing cations and anions.

Analysis of Options:

A. \(NaCl\): Both \(Na^+\) and \(Cl^-\) have sizes similar to \(Ag^+\) and \(Cl^-\), respectively. However, \(NaCl\) has a \(1:1\) stoichiometry (one sodium ion for every chloride ion). Adding \(NaCl\) wouldn't introduce vacancies in equal numbers (it would only create cation vacancies). So, \(NaCl\) is unlikely to cause Schottky defects in \(AgCl\).

B. \(CdCl_2\): \(Cd^{2+}\) is larger than \(Ag^+\), but \(Cl^-\) remains similar. The \(2:1\) charge ratio in \(CdCl_2\) allows for the introduction of two \(Cl^-\) ions (filling anion vacancies) for every \(Cd^{2+}\) ion (creating cation vacancies). This maintains charge balance and can contribute to Schottky defects.

C. \(CaCl_2\): \(Ca^{2+}\) is larger than \(Ag^+\), but \(Cl^-\) remains similar. Similar to \(CdCl_2\), the \(2:1\) charge ratio in \(CaCl_2\) allows for the introduction of two \(Cl^-\) ions (filling anion vacancies) for every \(Ca^{2+}\) ion (creating cation vacancies), potentially causing Schottky defects.

D. \(KCl\): \(K^+\) is slightly larger than \(Ag^+\), but \(Cl^-\) remains similar. Like \(NaCl\), \(KCl\) has a \(1:1\) stoichiometry, and adding it wouldn't introduce vacancies in equal numbers. So, \(KCl\) is unlikely to cause Schottky defects in \(AgCl\).

Based on the ionic size ratio and charge balance considerations, \(CdCl_2\) and \(CaCl_2\) are more likely to introduce Schottky defects in \(AgCl\) crystals due to their ability to create equal numbers of cation and anion vacancies. \(NaCl\) and \(KCl\) are less likely to do so.