Final answer:
The atomic weight of the element that crystallizes in a body-centered cubic unit cell with a density of 5.71 g/cm³ and a radius of 1.34Å is approximately 136.53 g/mol.
Step-by-step explanation:
The atomic weight of an element can be calculated by using the density, crystal structure, and atomic radius of the element. Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å. To determine the atomic weight, we first need to find the atomic radius of barium in this structure. The atomic radius can be calculated by dividing the edge length of the unit cell by 2√3. So, in this case, the atomic radius of barium is 5.025 Å / (2√3) = 2.05 Å. Now, we can use the atomic radius and the density (5.71 g/cm³) to find the atomic weight. The formula for density is mass/volume. Since the unit cell in a body-centered cubic structure contains two atoms, the volume of the unit cell is (edge length)³/2. The mass of the unit cell can be calculated by multiplying the volume by the density. Substituting these values in the formula, we get (2 * atomic weight) / ((2.05 Å)^3 * 0.5) = (5.71 g/cm³). Solving for the atomic weight, we get approximately 136.53 g/mol. Therefore, the correct answer is (d) 136.53 g/mol.