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).

Solution

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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The Solid State

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).

Some More Questions From The Solid State Chapter

Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Why is glass considred a super-cooled liquid?

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Classify the following solids in different categories based on the nature of intermolecular forces operating in them:
Potassium sulphate, tin, benzene, urea, ammonia, water, zinc
sulphate, graphite, rubidium, argon, silicon carbide.

Solid A is a very hard, electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it?

Ionic solids conduct electricity in liquid state but not in solid state. Explain.

What type of solids are electrical conductors, malleable and ductile?

Give the significance of a 'lattice point'.

Name the parameters that characterize a unit cell.

Distinguish between Hexagonal and monoclinic unit cells.

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For Daily Free Study Material Join wiredfaculty

The Solid State

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).

Some More Questions From The Solid State Chapter

Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Why is glass considred a super-cooled liquid?

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Classify the following solids in different categories based on the nature of intermolecular forces operating in them: Potassium sulphate, tin, benzene, urea, ammonia, water, zinc sulphate, graphite, rubidium, argon, silicon carbide.

Solid A is a very hard, electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it?

Ionic solids conduct electricity in liquid state but not in solid state. Explain.

What type of solids are electrical conductors, malleable and ductile?

Give the significance of a 'lattice point'.

Name the parameters that characterize a unit cell.

Distinguish between Hexagonal and monoclinic unit cells.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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).

Classify the following solids in different categories based on the nature of intermolecular forces operating in them:
Potassium sulphate, tin, benzene, urea, ammonia, water, zinc
sulphate, graphite, rubidium, argon, silicon carbide.