solid states pearsons book

Question

Comprehension VIII

 A cubic unit cell contains manganese ions at the corners and fl uoride ions at the centre of each edge (Mn = 55, F = 19, NA = 6 × 1023).

23. What is the empirical formula?

(a) MnF (b) MnF2 (c) MnF3 (d) MnF4

 24. What is the coordination number of the Mn ion?

 (a) 4 (b) 6 (c) 8 (d) 12

 25. The edge length of the unit cell, if the radius of Mn3+ ion is 0.65 Å and that of F− ion is 1.35 Å, is

 (a) 2.00 Å (b) 4.00 Å (c) 3.82 Å (d) 1.30 Å

 26. The density of solid is

(a) 2.92 g/cm3 (b) 5.84 g/cm3 (c) 8.75 g/cm3 (d) 23.33 g/cm3

Answer 1

 (23) Number of `Mn^(3+)` ions at the corners `=8xx1//8=1`

Number of `F^(-)` ions at the centre of the faces `=6xx1//2=3`

Empirical formula `MnF_(3)`.

(24) C.N. of Mn ions = 6 (structure being face centred)

(25) `a=2(r^(+)-r^(-))=2(0.65+1.35)=4.0Å`.