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: Identify the lattice type.
Polonium crystallises in a simple cubic (primitive) structure, where atoms sit only at the eight corners of the cube.
Step 2: See where atoms touch.
In a simple cubic cell, neighbouring corner atoms touch each other directly along the cube edge.
Step 3: Relate edge length to radius.
Along one edge you have half of one corner atom, a full gap of contact, and half of the next corner atom, which adds up to two radii. So $a = 2r$.
Step 4: Solve for the radius.
Rearranging gives $r = \dfrac{a}{2}$.
Step 5: Plug in the edge length.
$r = \dfrac{336}{2} = 168\text{ pm}$.
Step 6: Confirm the choice.
The atomic radius is 168 pm, matching option (2). The value 84 pm wrongly divides by 4, and 336 pm forgets to halve.
\[ \boxed{r = 168\text{ pm}} \]