Answer:

The given information states that the density of aluminum metal is 2.72 g/cm3 and it crystallizes in a lattice with an edge length of 404 pm. We need to determine the type of unit cell formed by aluminum in its crystal lattice and its coordination number.

Unit Cell:
The density of a material is related to its molar mass and the volume of its unit cell. The molar mass of aluminum is 26.98 g/mol. To determine the volume of the unit cell, we can use the equation:

Density = (Molar Mass) / (Volume of Unit Cell)

2.72 g/cm3 = 26.98 g/mol / (Volume of Unit Cell)

Volume of Unit Cell = 26.98 g/mol / 2.72 g/cm3

The g units cancel out, and we are left with cm3 as the unit for volume. Dividing the values, we get:

Volume of Unit Cell = 9.92 cm3/mol

Face Centered Cubic (FCC) Unit Cell:
The volume of a face-centered cubic (FCC) unit cell can be calculated using the equation:

Volume of FCC Unit Cell = (4 * Al) / (Avogadro's Number)

where Al is the edge length of the unit cell and Avogadro's Number is approximately 6.022 × 10^23 mol-1.

Substituting the given value of Al = 404 pm = 4.04 Å into the equation, we get:

Volume of FCC Unit Cell = (4 * (4.04 Å)^3) / (6.022 × 10^23 mol-1)

Converting the Ångstrom (Å) unit to centimeters (cm), we have:

1 Å = 1 × 10^-8 cm

Therefore, the volume of the FCC unit cell in cm3 is:

Volume of FCC Unit Cell = (4 * (4.04 × 10^-8 cm)^3) / (6.022 × 10^23 mol-1)

Volume of FCC Unit Cell = 6.73 × 10^-24 cm3/mol

Comparing this with the calculated volume of the unit cell for aluminum, we can see that they are not equal. Therefore, aluminum does not form a face-centered cubic (FCC) unit cell.

Conclusion:
Based on the above analysis, we can conclude that the correct alternative is option 'B': Aluminum forms a face-centered cubic (FCC) unit cell.

Coordination Number:
The coordination number is the number of atoms or ions that surround a central atom or ion in a crystal lattice. In an FCC unit cell, each corner atom is shared by eight unit cells, and each face-centered atom is shared by two unit cells. Therefore, the coordination number for an FCC lattice is 12.

Since aluminum forms an FCC unit cell, the coordination number for aluminum is 12, which is not listed in the given options. Therefore, none of the provided options correctly state the coordination number for aluminum.