The decreasing order of density of different crystals is

Options

A. f.c.c. `gt` b.c.c. `gt` simple cube
B. b.c.c. `gt` f.c.c. `gt` simple cube
C. simple cube `gt` f.c.c. `gt` b.c.c.
D. h.c.p. `gt` f.c.c. `gt` simple cube

Answer

To determine the decreasing order of density of different types of crystals, we need to analyze the packing efficiency of each crystal structure. Here’s a step-by-step solution:

### Step 1: Understand Crystal Structures
There are different types of crystal structures, namely:
- Face-Centered Cubic (FCC)
- Body-Centered Cubic (BCC)
- Simple Cubic (SCC)

### Step 2: Determine Packing Efficiency
The packing efficiency is the fraction of volume in a crystal structure that is occupied by the constituent particles (atoms, ions, or molecules). The packing efficiencies for the different structures are:
- **FCC**: Approximately 74%
- **BCC**: Approximately 68%
- **SCC**: Approximately 52%

### Step 3: Relate Packing Efficiency to Density
Density is directly related to packing efficiency. The higher the packing efficiency, the higher the density, assuming the mass of the particles is constant. Therefore, we can rank the crystal structures based on their packing efficiencies.

### Step 4: Order the Crystals by Density
Based on the packing efficiencies:
1. **FCC** has the highest packing efficiency (74%), hence it has the highest density.
2. **BCC** comes next with a packing efficiency of 68%.
3. **SCC** has the lowest packing efficiency (52%), thus it has the lowest density.

### Conclusion
The decreasing order of density of different crystals is:
1. FCC (Face-Centered Cubic)
2. BCC (Body-Centered Cubic)
3. SCC (Simple Cubic)

### Final Answer
The correct order is: **FCC > BCC > SCC**

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