Question

Calculate the edge length of unit cell if metal having atomic radius 170 pm forms simple cubic unit cell.

• A. $1.17 \times 10^{-8}$ cm
• B. $3.40 \times 10^{-8}$ cm
• C. $5.12 \times 10^{-8}$ cm
• D. $6.81 \times 10^{-8}$ cm

Hint:

SC: $a=2r$; BCC: $a = \frac{4r}{\sqrt{3}}$; FCC: $a = \sqrt{8}r$.

Answer 1

The Correct Option is B

Step 1: Formula
For a simple cubic (SC) unit cell, edge length $a = 2r$.

Step 2: Calculation
Given $r = 170$ pm.
$a = 2 \times 170$ pm = $340$ pm.

Step 3: Unit Conversion
$1$ pm = $10^{-10}$ cm.
$a = 340 \times 10^{-10}$ cm = $3.40 \times 10^{-8}$ cm.

Step 4: Conclusion
The edge length is $3.40 \times 10^{-8}$ cm.
Final Answer: (B)