Sodium has body centred packing. Distance between two nearest atoms is `3.7 Å`. The lattice parameter is

Options

A. `6.8 Å`
B. `4.3 Å`
C. `3.0 Å`
D. `8.6 Å`

Answer

To find the lattice parameter \( a \) for sodium, which has a body-centered cubic (BCC) structure, we can use the relationship between the nearest neighbor distance \( b \) and the lattice parameter \( a \).

### Step-by-Step Solution:

1. **Understanding the BCC Structure**:
In a body-centered cubic (BCC) structure, there are two atoms per unit cell: one at each corner of the cube and one in the center. The nearest neighbor distance \( b \) is the distance between the atom at the center and one of the corner atoms.

2. **Formula for Nearest Neighbor Distance**:
The relationship between the nearest neighbor distance \( b \) and the lattice parameter \( a \) for a BCC structure is given by the formula:
\[ b = \frac{\sqrt{3}}{2} a \]

3. **Rearranging the Formula**:
To find the lattice parameter \( a \), we can rearrange the formula:
\[ a = \frac{2b}{\sqrt{3}} \]

4. **Substituting the Given Value**:
We are given that the distance between two nearest atoms \( b \) is \( 3.7 \, \text{Å} \). We can substitute this value into the rearranged formula:
\[ a = \frac{2 \times 3.7 \, \text{Å}}{\sqrt{3}} \]

5. **Calculating the Value**:
Now, we calculate \( a \):
\[ a = \frac{7.4 \, \text{Å}}{\sqrt{3}} \approx \frac{7.4 \, \text{Å}}{1.732} \approx 4.27 \, \text{Å} \]

6. **Final Result**:
Rounding off, we can say that the lattice parameter \( a \) is approximately \( 4.3 \, \text{Å} \).

### Conclusion:
The lattice parameter \( a \) for sodium with a body-centered cubic structure, given the nearest neighbor distance of \( 3.7 \, \text{Å} \), is approximately \( 4.3 \, \text{Å} \).