The neon atoms has a radius of 160pm. What is the edge of the unit cell of a face centered structure of neon?

Options

A. 490pm
B. 320pm
C. 453pm
D. 481pm

Answer

To find the edge length of the unit cell of a face-centered cubic (FCC) structure of neon, we can follow these steps:

### Step 1: Understand the Structure
In a face-centered cubic (FCC) structure, atoms are located at each corner of the cube and at the center of each face. Each corner atom is shared by eight adjacent unit cells, and each face-centered atom is shared by two unit cells.

### Step 2: Relate Atomic Radius to Edge Length
In an FCC structure, the relationship between the atomic radius (r) and the edge length (a) of the unit cell can be expressed as:
\[ 4r = \sqrt{2}a \]
This equation arises because the face diagonal of the cube spans across four atomic radii (two radii from the corner atom and two from the face-centered atom).

### Step 3: Rearranging the Equation
We can rearrange the equation to solve for the edge length (a):
\[ a = \frac{4r}{\sqrt{2}} \]

### Step 4: Substitute the Given Radius
Given that the radius of a neon atom (r) is 160 pm, we can substitute this value into the equation:
\[ a = \frac{4 \times 160 \, \text{pm}}{\sqrt{2}} \]

### Step 5: Calculate the Edge Length
Now, calculate the value:
1. Calculate \( 4 \times 160 \):
\[ 4 \times 160 = 640 \, \text{pm} \]
2. Calculate \( \sqrt{2} \):
\[ \sqrt{2} \approx 1.414 \]
3. Divide 640 by \( \sqrt{2} \):
\[ a = \frac{640}{1.414} \approx 452.616 \, \text{pm} \]

### Final Answer
Thus, the edge length of the unit cell of a face-centered structure of neon is approximately **452.62 pm**.

---