Question

Calculate the volume of bcc unit cell if radius of an atom present in it is \( 1.86 \times 10^{-8} \) cm.

• A. \( 5.391 \times 10^{-23}\text{ cm}^{3} \)
• B. \( 8.995 \times 10^{-23}\text{ cm}^{3} \)
• C. \( 7.951 \times 10^{-23}\text{ cm}^{3} \)
• D. \( 6.453 \times 10^{-23}\text{ cm}^{3} \)

Hint:

For BCC: $a = \frac{4r}{\sqrt{3}}$. For FCC: $a = 2\sqrt{2}r$.

Answer 1

The Correct Option is C

Step 1: BCC Relation
In BCC, $4r = \sqrt{3}a \implies a = \frac{4r}{\sqrt{3}}$.
Step 2: Find Edge Length ($a$)
$a = \frac{4 \times 1.86 \times 10^{-8}}{1.732} \approx 4.295 \times 10^{-8}$ cm.
Step 3: Calculate Volume ($V = a^3$)
$V = (4.295 \times 10^{-8})^3 \approx 7.92 \times 10^{-23}$ cm$^3$.
Step 4: Conclusion
Based on the options, 7.951 is the closest value.
Final Answer:(C)