Lithium metal crystallizes in a body centred cubic crystals. If the length of the side of the unit cell of lithium is `351p m` the atomic radius of the lithium will be

Options

A. 152 pm
B. 75 pm
C. 300 pm
D. 240 pm

Answer

To find the atomic radius of lithium in a body-centered cubic (BCC) crystal structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the BCC Structure**: In a BCC unit cell, there are two atoms per unit cell: one at the center and one at each corner. The body diagonal of the cube contains three atomic radii (2 radii from the corner atoms and 1 radius from the center atom).

2. **Identify the Relationship**: The relationship between the edge length (a) of the unit cell and the atomic radius (r) in a BCC structure can be expressed using the formula:
\[ \text{Body Diagonal} = \sqrt{3}a = 4r \]
This means that the body diagonal is equal to four times the atomic radius.

3. **Rearrange the Formula**: From the above relationship, we can derive the formula for the atomic radius:
\[ r = \frac{\sqrt{3}}{4}a \]

4. **Substitute the Given Value**: The problem states that the edge length (a) of the lithium unit cell is 351 picometers. We can now substitute this value into the formula:
\[ r = \frac{\sqrt{3}}{4} \times 351 \text{ pm} \]

5. **Calculate the Radius**: Now, we perform the calculation:
- First, calculate \(\sqrt{3} \approx 1.732\).
- Then, calculate:
\[ r = \frac{1.732}{4} \times 351 \]
\[ r \approx 0.433 \times 351 \approx 152.133 \text{ pm} \]

6. **Final Result**: Rounding this to the nearest whole number, we find that the atomic radius of lithium is approximately:
\[ r \approx 152 \text{ pm} \]

### Conclusion:
The atomic radius of lithium is **152 picometers**.