Question

iron has a bcc crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. compute its theoretical density. (Avogadro's Number =6.023×10²³atoms /mol )

Answer 1

The question pertains to the calculation of theoretical density of iron using its atomic radius, atomic weight, and Avogadro's number, considering its bcc crystal structure.

Step-by-step explanation:

The student is asking how to compute the theoretical density of iron, which has a body-centered cubic (bcc) crystal structure, an atomic radius, and an atomic weight. To find the theoretical density, we need to calculate the volume of the unit cell and then use the atomic weight and Avogadro's number to find the mass of iron atoms within that cell.

Iron has a bcc structure, meaning there are 2 atoms per unit cell. The atomic radius (r) is given as 0.124 nm, and we can calculate the cell edge length (a) for a bcc crystal using the relationship a = 4r/√3. Once the edge length is known, we can calculate the volume of the unit cell (V_cell = a^3). The density (ρ) can then be found using the formula ρ = (mass of atoms in the cell) / (volume of the cell), where the mass of atoms in the cell is calculated by multiplying the number of atoms in the cell by the atomic weight and dividing by Avogadro's number.