Strontium crystallizes in a fcc unit cell with edge length a. it contains 0.2% Frenkel defect and another crystal of Sr contains 0.1% Schottky defect. Density of solid with Frenkel defect=`d_(f)` and density with Schottky defect=`d_(S)`, then

Options

A. `d_(f)=d_(S)`
B. `d_(f) gt d_(S)`
C. `d_(f) lt d_(S)`
D. `d_(f)=2d_(S)`

Answer

To solve the problem, we need to analyze the effects of Frenkel and Schottky defects on the density of strontium crystals.

### Step-by-Step Solution:

1. **Understanding the Unit Cell and Density**:
- Strontium crystallizes in a face-centered cubic (FCC) structure. In an FCC unit cell, there are 4 formula units of the substance per unit cell.
- The density (\(d\)) of a crystal can be calculated using the formula:
\[ d = \frac{Z \cdot M}{N_A \cdot a^3} \]
where \(Z\) is the number of formula units per unit cell, \(M\) is the molar mass, \(N_A\) is Avogadro's number, and \(a\) is the edge length of the unit cell.

2. **Frenkel Defect**:
- In a Frenkel defect, smaller cations move to interstitial sites, but no atoms leave the crystal lattice. Thus, the mass of the crystal remains the same.
- Therefore, the density of the crystal with a Frenkel defect (\(d_f\)) remains unchanged:
\[ d_f = \frac{Z \cdot M}{N_A \cdot a^3} \]

3. **Schottky Defect**:
- In a Schottky defect, equal numbers of cations and anions leave the lattice, which decreases the total mass of the crystal.
- If \(x\) is the fraction of the total number of cations and anions that leave the lattice, the effective number of formula units in the unit cell decreases.
- For a Schottky defect with 0.1% defect, the new effective number of formula units (\(Z_s\)) can be calculated as:
\[ Z_s = Z \cdot (1 - 0.001) = 4 \cdot 0.999 = 3.996 \]
- The density of the crystal with a Schottky defect (\(d_s\)) is:
\[ d_s = \frac{Z_s \cdot M}{N_A \cdot a^3} = \frac{3.996 \cdot M}{N_A \cdot a^3} \]

4. **Comparing Densities**:
- Since \(d_f\) remains the same and \(d_s\) is reduced due to the loss of mass:
\[ d_f > d_s \]
- Therefore, the density of the crystal with a Frenkel defect is greater than that with a Schottky defect.

### Conclusion:
The relationship between the densities is:
\[ d_f > d_s \]