Question

Units:
NA= 6.02×1023 atoms/mol

Walter White who lives in Simeranya (a utopic city in Anarres) prepares blue crystals, named as myth, which adopt a side-centered cubic (scc) cell with a molecular formula of A.B Side-centered cubic (scc) cell Top view 1. Determine the molecular formula of myth. 2. Calculate the atomic packing factor (APF) of scc unit cell. The atomic radii of A and B are equal to 120 and 132 pm, respectively. 3. Calculate the density of the myth molecule. The atomic masses of A and B are equal to 58 and 60 g.mol1, respectively. 4. Determine the coordination numbers of A and B. 5. Calculate the planar densities (in atoms/nm2) of the following the crystallographic planes; (100), (111), and (202). , Determine the diffraction angle for the molecule, which corresponds to (002) and (200) planes? Units NA- 6.02x10 atoms/mol

Answer 1

Question 1.

The molecular formula of the myth can be written as follows.

A-atoms occupy all the 12 edge-centers.

The contribution by each edge-center = 1/4

Therefore, no. of atoms 'A' = 12*1/4 = 3

B-atom occupies the body-center.

The contribution by body-center = 1

Therefore, no. of atoms 'B' = 1*1 = 1

Therefore, the formula of the myth = A₃B

Question 2.

The atomic packing factor (APF) of the unit cell = (Z*4/3 $\pi$r³)/a³

Where Z = no. of atoms per unit cell = 3 + 1 = 4

'r' is the radius of the unit cell

'a' is the edge length of the unit cell

'a³' is the total volume of the unit cell

Question 3.

The density of the unit cell (d) = ZM/N_A.a³

Here, M = molar mass of A₃B = 3*58 + 60 = 234 g/mol

NA is Avagadro's number = 6.02*10²³ atoms/mol

'a' is the edge-length of the unit cell

Question 4.

The coordination number of B = 12