Question

Calculate the atomic radius of an element having edge length \(3.61\times 10^{-8}\ \text{cm}\) for fcc structure.

• A. \(1.43\times 10^{-8}\ \text{cm}\)
• B. \(1.28\times 10^{-8}\ \text{cm}\)
• C. \(0.90\times 10^{-8}\ \text{cm}\)
• D. \(1.02\times 10^{-8}\ \text{cm}\)

Hint:

In fcc, atoms touch along the face diagonal, so r equals the edge length times root 2 divided by 4.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In an fcc cell the atoms touch along the face diagonal, so \(4r = \sqrt{2}\,a\).

Step 2: Radius formula
\(r = \dfrac{a}{2\sqrt{2}} = \dfrac{\sqrt{2}\,a}{4}\).

Step 3: Calculation
\(r = \dfrac{1.414\times3.61\times10^{-8}}{4} = 1.28\times10^{-8}\ \text{cm}\).

Final Answer:
The atomic radius is 1.28 times 10 to the power minus 8 cm. \[ \boxed{\text{(B) }1.28\times 10^{-8}\ \text{cm}} \]