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The Solid State

Short Answer Type

241. Aluminium forms fcc cubic crystals. The density of aluminium is 2.7 g cm^–3. Calculate the length of the edge of the unit cell of Al.

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242. The density of KBr is 2.75 g cm^–3. The length of the edge of the unit cell is 654 pm. Show that KBr has a fcc structure.

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243. Tungsten has a density of 19.35 g cm^–3 and the length of the side of the unit cell is 316 pm. The unit cell is a body centred unit cell. How many atoms does 50 grams of the element contain ?

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244. In the cubic crystal of CsCl (d = 3.97 g cm^–3), the eight corners are occupied by CI^–with a Cs⁺ at the centre and vice versa. Calculate the distance between the neighbouring Cs⁺ and CI^– ions. What is the radius ratio of the two ions ? (At. mass of Cs = 132.91 and CI = 35.45).

In a unit cell there are one Cs and 1 x 8/8 =1 chlorine (Cl^-) such that one CsCl molecule

therefore
As we have given
density = 3.97 g cm^-3
Mass of CsCl = 168.36g
Number of unit cell(Z) = 1

$apply formula d = \frac{Z xM}{a^{3} x N_{A}} 3.97 = \frac{1 x 168.36}{a^{3} x 6.023 x 10^{23}} a = 4.13 x 10^{- 8} cm a = 4.13 A^{0}$

for a cube of side length 4.13A⁰ diagonal

= $\sqrt{3 a} i . e ., \sqrt{3 x 4.13} = 7.15 A^{0}$

as it is a BCC with Cs⁺ at centre radius r⁺ and Cl^- at corner radius r^- so,

2r⁺ +2r^- =7.15 or r⁺ +r^- =3.57A⁰

such that distance between neighbouring Cs⁺ and Cl^- =3.57A⁰

now assume two Cl^- ion touch with each other so length of unit cell = 2r^- =4.13
r^- =2.06A⁰
r⁺ =3.57 -2.06 =1.51

r+/r-=1.51/2.06 =0.73

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Long Answer Type

245. How the crystalline solids are classified on the basis of the nature of bonding? Give suitable examples and nature of the forces present in different types of solids.

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246. Write two important features, coordination numbr of the ions and number of formula units per unit cell for the following crystals:
(i) Cesium chloride, (ii) Zinc sulphide, (iii) Calcium fluorite, (iv) Sodium oxide.

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247. Explain the reasons why:
(a) Frenkel defect is not found in pure alkali halides?
(b) Zinc oxide appears yellow on heating?
(c) Solid containing F-centres are para magnetic?
(d) Uncharged atoms or molecules never crystallize in a simple cubic structure?
(e) A given element will have the same density in both a hexagonal close-packed structure and a cubic close-packed structure?

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Short Answer Type

248.

What is the formula of a compound in which the element Y forms ccp lattice and atoms of X occupy 1/3^rd of tetrahedral voids?

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249.

An element with molar mass 27 g mol^-1 forms a cubic unit cell with edge length 4.05 x 10^-8 cm . If its density is 2.7 g cm^-3, what is the nature of the cubic unit cell?

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