Edge length of unit cell of Chromium metal is 287 pm with the arrangement. The atomic radius is the order of:

Options

A. 124.27 pm
B. 287 pm
C. 574 pm
D. 143.6 pm

Explanation

To find the atomic radius of Chromium metal given its edge length in a Body-Centered Cubic (BCC) structure, we can follow these steps:

### Step 1: Understand the BCC Structure
In a BCC unit cell, there are atoms located at the eight corners of the cube and one atom at the center of the cube. The arrangement is such that the atoms at the corners and the center are in contact along the body diagonal of the cube.

**Hint:** Recall that in a BCC structure, the atoms at the corners and the center are arranged in a specific way that allows us to derive a relationship between the atomic radius and the edge length.

### Step 2: Identify the Relationship Between Atomic Radius and Edge Length
For a BCC unit cell, the relationship between the atomic radius (R) and the edge length (A) is given by the formula:
\[ R = \frac{\sqrt{3}}{4} A \]

**Hint:** This formula is derived from the geometry of the BCC unit cell, where the body diagonal can be expressed in terms of the edge length and the atomic radius.

### Step 3: Substitute the Given Edge Length
We are given the edge length (A) of Chromium metal as 287 pm (picometers). We can substitute this value into the formula:
\[ R = \frac{\sqrt{3}}{4} \times 287 \, \text{pm} \]

**Hint:** Make sure to perform the multiplication carefully and remember to calculate the square root of 3.

### Step 4: Calculate the Atomic Radius
Now, we perform the calculation:
1. Calculate \(\sqrt{3} \approx 1.732\).
2. Multiply by 287 pm:
\[ R = \frac{1.732}{4} \times 287 \]
\[ R = 0.433 \times 287 \]
\[ R \approx 124.27 \, \text{pm} \]

**Hint:** Double-check your calculations to ensure accuracy, especially in the multiplication step.

### Step 5: Conclusion
The atomic radius of Chromium metal is approximately 124.27 pm.

**Final Answer:** The atomic radius is in the order of 124 pm.