For the closest packing of atoms A (radius, `r_(A)`), the maximum radius of atom B that can be fitted into octahedral void is

Options

A. 0.155 `r_(A)`
B. 0.125 `r_(A)`
C. 0.414 `r_(A)`
D. 0.732 `r_(A)`

Answer

To find the maximum radius of atom B that can fit into the octahedral void formed by the closest packing of atoms A (with radius \( r_A \)), we can follow these steps:

### Step 1: Understand the Structure of Closest Packing
In closest packing arrangements, atoms are packed in such a way that they occupy the maximum available space. The two common types of closest packing are face-centered cubic (FCC) and hexagonal close packing (HCP).

**Hint:** Remember that in closest packing, atoms are arranged to minimize empty space.

### Step 2: Identify the Octahedral Voids
In a closest packed structure, octahedral voids are formed between the atoms. Each octahedral void is surrounded by six atoms.

**Hint:** Visualize the arrangement of atoms to see where the voids are located.

### Step 3: Determine the Size of the Octahedral Void
The radius of the octahedral void can accommodate a smaller atom (B). The relationship between the radius of atom A (\( r_A \)) and the radius of the octahedral void (\( r_{void} \)) can be established. The maximum radius of atom B that can fit into the octahedral void is given by the range of radii for octahedral voids.

**Hint:** Recall the specific range for octahedral voids in terms of the radius of atom A.

### Step 4: Use the Radius Ratio
For octahedral voids, the maximum radius of atom B that can fit is approximately 0.414 times the radius of atom A. This means:

\[ r_B = 0.414 \times r_A \]

**Hint:** This ratio helps you determine the maximum size of atom B in relation to atom A.

### Step 5: Conclusion
Thus, the maximum radius of atom B that can be fitted into the octahedral void formed by the closest packing of atoms A is:

\[ r_B = 0.414 \times r_A \]

**Final Answer:** The maximum radius of atom B that can fit into the octahedral void is \( 0.414 \times r_A \).

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