Question

Calculate the edge length of bcc unit cell if radius of a particle present in it is 186 pm.

• A. $4.296\times10^{-8}$ cm
• B. $7.301\times10^{-8}$ cm
• C. $3.715\times10^{-8}$ cm
• D. $5.419\times10^{-8}$ cm

Hint:

Radius-Edge Length Relationships to memorize:
Simple Cubic (sc): $a = 2r$
Face-Centered Cubic (fcc): $a = 2\sqrt{2}r$
Body-Centered Cubic (bcc): $a = \frac{4r}{\sqrt{3}}$

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In a body-centered cubic (bcc) unit cell, the particles touch along the body diagonal. The relationship between edge length ($a$) and radius ($r$) is unique to this geometry.

Step 2: Formula Application:
For bcc: $\sqrt{3}a = 4r \implies a = \frac{4r}{\sqrt{3}}$

Step 3: Explanation:
Given $r = 186$ pm. $$a = \frac{4 \times 186}{1.732} = \frac{744}{1.732} \approx 429.56 \text{ pm}$$ To convert to cm: $429.56 \times 10^{-10}$ cm = $4.296 \times 10^{-8}$ cm.

Step 4: Final Answer:
The edge length is 4.296 $\times$ 10$^{-8}$ cm.