This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and the formula for density. The atomic mass (M) of the element is 100 \, g/mol. The unit cell edge length (a) is 400 \, pm. The crystal structure is Body-Centered Cubic (BCC), for which the number of atoms per unit cell (Z) is 2. Avogadro's number (N_A) is 6.022 × 10^23 \, mol^-1. The formula for the density () of a unit cell is: = (Z × M)/(a^3 × N_A) Step 2: Convert the unit cell edge length from picometers (pm) to centimeters (cm). 1 \, pm = 10^-10 \, cm a = 400 \, pm = 400 × 10^-10 \, cm = 4 × 10^-8 \, cm Step 3: Calculate the volume of the unit cell (a^3). a^3 = (4 × 10^-8 \, cm)^3 = 4^3 × (10^-8)^3 \, cm^3 = 64 × 10^-24 \, cm^3 Step 4: Substitute the values into the density formula and calculate. = 2 × 100 \, g/mol(64 × 10^-24 \, cm^3) × (6.022 × 10^23 \, mol^-1) = 200 \, g64 × 6.022 × 10^-24+23 \, cm^3 = 200 \, g64 × 6.022 × 10^-1 \, cm^3 = 200 \, g385.408 × 10^-1 \, cm^3 = 200 \, g38.5408 \, cm^3 ≈ 5.188 \, g/cm^3 Step 5: Compare the calculated density with the given options. The calculated density is 5.188 \, g/cm^3, which matches option (c). The final answer is c) 5.188 \, g/cm^3.