BCC crystal structure, atomic radius of .1363, and an atomic weight of 95.94g/mol. How would you compute the theoretical density?
radius is 0.1363 WHAT? What unit?
My best guess is that this is 136.3 pm which converts to 136.3 x 10^-9 m or 1.363 x 10^-8 cm.
Then d (the diagonal in the bcc) is
4r = 4 x 1.353 x 10^-8 = 4.452 x 10^-8 cm
and d^2 = 3a^2.
Solve for a and I get 3.148 x 10^-8 cm and volume is a^3 = ??
mass of unit cell is 2 atoms/unit cell x 95.94/6.022 x 10^23 = ??
Then density = mass/volume. I get about 10.2. Check my thinking. Check my arithmetic.
You may want to note that I made a typo in converting pm to cm in the first step; however, the answer of 1.363 x 10^-8 cm is correct.
To compute the theoretical density of a material with a Body-Centered Cubic (BCC) crystal structure, we need to know the atomic radius and the atomic weight of the material. The theoretical density is calculated using the following formula:
Theoretical Density = (Z * M) / (a^3 * N_A)
Where:
- Z is the number of atoms per unit cell (for BCC, Z = 2),
- M is the atomic weight of the material (given as 95.94 g/mol),
- a is the length of one edge of the unit cell, and
- N_A is Avogadro's number (6.022 × 10^23 atoms/mol).
You provided the atomic radius as 0.1363 units. However, we also need the unit of measurement for the atomic radius (e.g., picometers, angstroms, or nanometers) to calculate the edge length 'a' properly.
Please provide the unit of measurement for the atomic radius so that we can proceed with the calculation.