Polonium crystallizes in a simple cubic strtucture. The edge of the unit cell is 0.236nm. What is the radius of the polonium atoms:

Options

A. 0.144 nm
B. 0.156 nm
C. 0.118 nm
D. 0.102 nm

Answer

To find the radius of polonium atoms in a simple cubic structure, follow these steps:

### Step 1: Understand the Simple Cubic Structure
In a simple cubic unit cell, atoms are located at each of the eight corners of the cube. Each corner atom contributes 1/8th of its volume to the unit cell.

### Step 2: Identify the Relationship Between Edge Length and Atomic Radius
In a simple cubic structure, the edge length (a) of the unit cell is related to the atomic radius (r) by the equation:
\[ a = 2r \]
This equation arises because the distance between the centers of two adjacent atoms (which are touching) is equal to the edge length of the unit cell.

### Step 3: Use the Given Edge Length
The edge length of the unit cell is given as:
\[ a = 0.236 \, \text{nm} \]

### Step 4: Rearrange the Equation to Find the Radius
To find the radius (r), rearrange the equation:
\[ r = \frac{a}{2} \]

### Step 5: Substitute the Edge Length into the Equation
Now substitute the given edge length into the equation:
\[ r = \frac{0.236 \, \text{nm}}{2} \]

### Step 6: Calculate the Radius
Perform the calculation:
\[ r = 0.118 \, \text{nm} \]

### Conclusion
The radius of the polonium atoms is:
\[ r = 0.118 \, \text{nm} \]