Final answer:
To calculate the edge length 'a' of the unit cell in an FCC structure from the atomic radius 'r' of 130 pm, we use the relationship 4r = √2 * a. Solving gives us an edge length of approximately 367.7 pm, and the closest given option is B. 330 pm.
Step-by-step explanation:
An element crystallizes in the Face-Centered Cubic (FCC) structure. To find the edge length of the unit cell given the atomic radius of 130 pm, we would use the geometric relation between the radius and the edge length in an FCC lattice. From geometry, we know that the diagonal of one face of the cube, which is √2 times longer than the edge, is equal to four atomic radii since the atoms touch each other along the diagonals in an FCC structure.
The relationship is given by:
4r = √2 * a,
where 'r' is the atomic radius and 'a' is the edge length. Substituting the given atomic radius:
4 * 130 pm = √2 * a,
520 pm = √2 * a,
Divide both sides by √2 to solve for 'a':
a = 520 pm / √2 ≈ 367.7 pm.
Looking at the options provided, the closest value to our calculated result is 330 pm, so the answer is:
B. 330 pm