If atomic radius of barium is `2.176Å` and it crystallises in b.c.c. unit cell, the edge length of unit cell is

Options

A. `3.512Å`
B. `2.483Å`
C. `5.025Å`
D. None of these

Explanation

To find the edge length of a barium unit cell that crystallizes in a body-centered cubic (BCC) structure, we can follow these steps:

### Step 1: Understand the relationship between atomic radius and edge length in BCC
In a BCC unit cell, the relationship between the edge length (A) and the atomic radius (R) is given by the formula:
\[ \sqrt{3}A = 4R \]

### Step 2: Rearrange the formula to solve for edge length (A)
To find the edge length (A), we can rearrange the formula:
\[ A = \frac{4R}{\sqrt{3}} \]

### Step 3: Substitute the given atomic radius into the formula
We know the atomic radius of barium (R) is 2.176 Å. Substituting this value into the rearranged formula:
\[ A = \frac{4 \times 2.176 \, \text{Å}}{\sqrt{3}} \]

### Step 4: Calculate the value of \(\sqrt{3}\)
The value of \(\sqrt{3}\) is approximately 1.732.

### Step 5: Perform the calculation
Now we can calculate the edge length:
\[ A = \frac{4 \times 2.176}{1.732} \]
\[ A = \frac{8.704}{1.732} \]
\[ A \approx 5.025 \, \text{Å} \]

### Conclusion
Thus, the edge length of the barium BCC unit cell is approximately **5.025 Å**.

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