Calculate the edge length of unit cell if a metal with atomic radius 128 pm forming fcc unit cell structure.

Step-by-step solution

In a face-centered cubic (FCC) structure, atoms contact along face diagonals. The length of the face diagonal equals 4r , where r is the atomic radius. The face diagonal is also given by 2 a from the Pythagorean theorem, equating to 4r = 2 a , so a = 2 2 r . Given r = 128 pm, substitute into the formula: a = 2 2 128 2 1.414 128 = 361.984 pm. Rounded, a 362 pm. Convert to centimeters using 1 pm = 10⁻¹⁰ cm, yielding a = 362 10⁻¹⁰ = 3.62 10⁻⁸ cm. This matches option A , so the final answer is A .