Question

Nickel crystallises in a fcc type of unit cell, with edge length 0.3524 nm. Calculate the radius of the nickel atom.

• A. 0.1624 nm
• B. 0.2164 nm
• C. 0.1426 nm
• D. 0.1246 nm

Hint:

In fcc unit cells, the relationship between edge length and atomic radius is \( a = 2\sqrt{2}r \).

Answer 1

The Correct Option is D

Step 1: Understanding the fcc unit cell.
In a face-centered cubic (fcc) unit cell, the relation between the edge length \( a \) and the atomic radius \( r \) is given by: \[ a = 2\sqrt{2}r \] Given that the edge length \( a = 0.3524 \, \text{nm} \), we can solve for \( r \).

Step 2: Solving for \( r \).
\[ r = \frac{a}{2\sqrt{2}} = \frac{0.3524}{2\sqrt{2}} = 0.1246 \, \text{nm} \]
Step 3: Conclusion.
The correct answer is (D) 0.1246 nm, which is the radius of the nickel atom.