Determine the inside angle of a shape with n sides. Find the APF of a BCC crysta
ID: 483449 • Letter: D
Question
Determine the inside angle of a shape with n sides. Find the APF of a BCC crystal structure. If the atomic radius of Al is 0.143nm, calculate the volume of its unit Cell. (answer in cubic meters, cm^3) Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. Compute and compare its theoretical density with the experimental value found inside the front cover of your text book. Calculate the radius of an iridium atom, given that Ir has an FCC crystal structure, a density of 22.4 g/cm3, and an atomic weight of 192.2 g/mol. A hypothetical metal has the simple cubic crystal structure shown to the right. If its atomic weight is 70.4 g/mol and the atomic radius is 0.126 nm, compute its density. Zirconium has an HCP crystal structure and a density of 6.51 g/cm3. What is the volume of its unit cell in cubic meters? If the ratio is 1 593, compute the values of c and a.Explanation / Answer
2. APF for BCC
length = 4R = sq.rt.(3)a
APF = volume of atoms/volume of unit cell
= 2(4/3)pi.(sq.rt.(3)a/4)^3/q^3
= 0.68
3. Al with atomic radius = 0.141 nm = 1.41 x 10^-8 cm
edge length (d) = 1.41 x 10^-8 x 2 x sq.rt.(2)
= 4 x 10^-8 cm
Volume = d^3 = (4 x 10^-8)^3 = 6.38 x 10^-23 cm^3
4. Fe with FCC, ratdius = 0.124 nm = 1.24 x 10^-8 cm
edge length (d) = 1.24 x 10^-8 x 2 x sq.rt.(2)
= 3.51 x 10^-8 cm
Volume = d^3 = (3.51 x 10^-8)^3 = 4.32 x 10^-23 cm^3
mass of unit cell = 4 x 55.85/6.023 x 10^23 = 3.71 x 10^-22 g/unit cell
density = mass/volume = 3.71 x 10^-22/4.32 x 10^-23 = 8.586 g/cm^3
Theoretical density = 7.87 which is lower than the density calculated above.
5. IR with FCC structure
density = 22.4 g/cm^3
mass of unit cell = 4 x 192.2/6.023 x 10^23 = 1.3 x 10^-21 g/unit cell
volume of unit cell = 1.3 x 10^-21/22.4 = 5.32 x 10^-22 cm^3
edge length = cube root(5.32 x 10^-22) = 8.10 x 10^-8 cm
radius = 8.10 x 10^-8/2 x sq.rt.(2) = 2.86 x 10^8 cm
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.