Question

For simple cubic crystal edge length is expressed as

• A. $a = 2r$
• B. $a = \frac{r}{2}$
• C. $a = \sqrt{2}r$
• D. $a = \frac{r}{\sqrt{2}}$

Hint:

Visualizing the lattice helps! A simple cubic cell is the most straightforward arrangement because there are no extra interior or face-centered atoms to push the corners apart. The edge is just two radii side-by-side!

Answer 1

The Correct Option is A

Step 1: Picture the simple cubic cell.
In a simple cubic lattice, identical atoms sit only at the eight corners of the cube. We must find how the edge length $a$ relates to the atomic radius $r$.
Step 2: Find where atoms touch.
Two corner atoms along the same edge are nearest neighbours and touch each other directly along that edge.
Step 3: Trace the edge.
Starting at one corner atom's centre and moving along the edge, we cross one radius to reach the contact point, then another radius to reach the next atom's centre.
Step 4: Add the radii.
The edge length is therefore $a = r + r$.
Step 5: Simplify.
$a = 2r$.
Step 6: Match the option.
The relation $a = 2r$ is option (1). The $\sqrt{2}$ and $\sqrt{3}$ forms belong to FCC and BCC, not simple cubic.
\[ \boxed{a = 2r} \]