A metal crystallizes in a face centered cubic structure and has a density of 11.9 g/cm³.If the radius of the metal atom is 138 pm,what is the identity of the metal? A) At B) Pd C) Mn D) Fe E) Cr

Question

Quizplus · Accepted Answer

Given: 
Density of metal = 11.9 g/cm³
Radius of metal atom = 138 pm = 1.38 Å

We know that in a face-centered cubic (fcc) structure, the atoms are arranged in such a way that each corner of the cube is shared by 8 atoms and each face of the cube is shared by another 6 atoms. The atoms touch each other along the face diagonal in an fcc structure.

Using the formula for the density of a fcc structure:

Density = (4 * atomic mass)/(avogadro's number * (radius of atom)³)

We can rearrange the formula to get:

Atomic mass = (Density * avogadro's number * (radius of atom)³)/4

Substituting the given values:

Atomic mass = (11.9 * 6.022 * 10²³ * (1.38)³)/4 = 106.5 g/mol

From the periodic table, we can see that the atomic mass of Pd (palladium) is very close to 106.5 g/mol. Therefore, the metal is most likely Pd.

A Metal Crystallizes in a Face Centered Cubic Structure and Has