Question

A metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is 408 pm. The diameter of the metal atom is:

• A. 228 pm
• B. 288 pm
  
• C. 144 pm
• D. 326 pm

Answer 1

The correct option is B 288 pm

Explanation:

A metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is $408pm$

For $FCC$ structure

Radius =$\frac{a}{a\sqrt{2}}$

Given $a=408pm$

r=$\frac{408}{a\sqrt{2}}=144pm$

we know that: Diameter=$2r$

so =2 x 144=288pm

Option b is correct answer