Question

What is the atomic radius of polonium if it crystallises in a simple cubic structure with edge length of unit cell 336 pm?

• A. 84 pm
• B. 168 pm
• C. 234 pm
• D. 336 pm

Hint:

Always remember the simple geometric relationships for cubic cells: Simple Cubic is $a = 2r$, Body-Centered Cubic (BCC) is $\sqrt{3}a = 4r$, and Face-Centered Cubic (FCC) is $\sqrt{2}a = 4r$. For simple cubic, just cut the edge length directly in half!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the unit cell edge length ($a = 336\text{ pm}$) for a polonium crystal that forms a simple cubic lattice. We need to determine its corresponding atomic radius ($r$).

Step 2: Key Formula or Approach:
In a simple cubic (SCC) crystal lattice structure, atoms touch each other along the edges of the cube. Therefore, the total edge length ($a$) of the unit cell is exactly equal to two times the atomic radius ($r$): $$a = 2r \implies r = \frac{a}{2}$$

Step 3: Detailed Explanation:
Given parameters: Edge length ($a$) = 336 pm Substitute this value into the geometric relation: $$r = \frac{336\text{ pm}}{2} = 168\text{ pm}$$

Step 4: Final Answer:
The atomic radius of polonium is 168 pm, matching option (B).