The Solid State

Let's analyze the characteristics of the Schottky defect.
The Schottky defect is a type of point defect in a crystal lattice.
(A) It is due to missing of equal number of cations and anions from lattice points: This is the definition of a Schottky defect. To maintain overall electrical neutrality, when a cation leaves its lattice site, an anion must also leave its site, creating a pair of vacancies. This statement is correct.
(B) On the whole crystal is electrically neutral: As explained above, an equal number of positive cations and negative anions are missing from the lattice. Therefore, the overall charge of the crystal remains balanced and it stays electrically neutral. This statement is correct.
(C) It is shown by ionic compounds in which cation and anion are of almost same size: This defect is common in highly ionic compounds where the cations and anions have similar sizes (i.e., a high coordination number). This similarity in size makes it equally probable for either ion to leave the lattice. Examples include NaCl, KCl, CsCl. This statement is correct.
(D) Density of the crystal increases: The Schottky defect involves the removal of ions from the crystal lattice, creating vacancies. Since mass is lost from the crystal while the volume remains essentially unchanged, the density of the crystal must decrease. Density = Mass/Volume. As Mass decreases, Density decreases. This statement is incorrect.
The question asks for the incorrect statement. Therefore, option (D) is the answer.

Step 1: Understanding the Concept:
The density of a crystal is determined by the mass of the atoms in its unit cell and the volume of the unit cell. Different crystal structures (like face-centered cubic, fcc, and body-centered cubic, bcc) have different numbers of atoms per unit cell and can have different unit cell volumes.
Step 2: Key Formula or Approach:
The formula for the density ( ) of a crystal is: where: - = number of atoms per unit cell - = molar mass of the element - = Avogadro's number - = edge length of the unit cell To find the ratio of densities , we can set up the ratio of their formulas. The terms and will cancel out as we are dealing with the same metal.
Step 3: Detailed Explanation:
First, identify the values for each structure:
- For fcc structure: - Number of atoms per unit cell, . - Edge length, Å. - For bcc structure: - Number of atoms per unit cell, . - Edge length, Å. Now, substitute these values into the ratio formula:
Now, perform the division:
This value is approximately 1.26.
Step 4: Final Answer:
The ratio of the densities of fcc and bcc is approximately 1.26. Therefore, option (B) is correct.