The actual density of a crystal of NaCl is observed to be lower than the expected value. It is caused
due to the presence of:

Schottky Defect

The correct answer is option 3. Schottky Defect.

Let us delve into each type of defect and how they affect the density of a crystal, focusing on why the Schottky defect specifically causes a decrease in density.

Schottky Defect

A Schottky defect is a type of point defect where equal numbers of cations and anions are missing from their regular lattice sites, creating vacancies.

Effect on Density:

Vacancies: The missing ions create vacancies in the lattice. Since the missing ions are not replaced by anything else, these vacancies lead to a reduction in the overall mass of the crystal without a corresponding reduction in volume. This results in a decrease in the crystal's density.

Density Calculation: Density (\(\rho\)) is defined as mass per unit volume (\(\rho = \frac{m}{V}\)). In the case of Schottky defects, since the mass of the crystal decreases due to the missing ions but the volume remains nearly the same (since the vacancies are quite small relative to the overall volume), the density decreases.

Frenkel Defect

A Frenkel defect involves the displacement of an ion from its normal lattice site to an interstitial site within the crystal.

Effect on Density:

Redistribution: In a Frenkel defect, an ion is not removed from the crystal but rather is displaced to an interstitial position. This keeps the total number of ions in the crystal constant, so the overall mass of the crystal remains the same.

Volume Consideration: Although the local arrangement of ions changes, the density remains largely unaffected because no ions are lost; they are simply relocated.

Interstitial Defect

An interstitial defect occurs when extra ions are introduced into the interstitial spaces between the regular lattice sites.

Effect on Density:

Increased Mass: Extra ions in interstitial sites increase the mass of the crystal. Since the volume does not expand proportionally to accommodate these extra ions, the density of the crystal actually increases rather than decreases.

Density Calculation: The addition of extra ions increases the numerator (mass) in the density formula, which results in an increase in density.

Impurity Defect

An impurity defect involves the substitution of some of the host atoms or ions with foreign atoms or ions.

Effect on Density:

Substitution: If the impurity ions are similar in size and mass to the host ions, the density may not change significantly. If the impurities are significantly different in size or mass, they could either increase or decrease the density depending on their characteristics.

Variable Impact: The impact on density due to impurity defects can vary based on the type and concentration of the impurity.

Summary

Schottky Defect is the primary defect causing a decrease in the density of the crystal. This is because it results in the removal of ions from the lattice, creating vacancies without compensating for the lost mass, thereby reducing the overall density of the crystal.

In contrast, Frenkel defects, interstitial defects, and impurity defects either do not significantly affect the density or have a different impact on it.