The Solid State

Question

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?

Solution

Molar mass of the given element, M = 27 g mol^-1 = 0.027 kg mol^-1

Edge length, a = 4.05 x 10^-8 cm = 4.05 x 10^-10 m

Density, d = 2.7 g cm^-3 = 2.7 x 10³ kg m^-3

Applying the relation,

$straight d space equals fraction numerator straight z space straight x space straight m over denominator straight a cubed space straight x space straight N subscript straight A end fraction$

Where, Z is the number of atoms in the unit cell and NA is the Avogadro number. Thus,

$straight Z equals space fraction numerator straight d space straight x space straight a cubed space straight x space straight N subscript straight A space over denominator straight m end fraction fraction numerator 2.7 space straight x space 10 cubed space straight x space left parenthesis 4.05 space straight x space 10 to the power of negative 10 end exponent right parenthesis cubed space straight x space 6.022 space straight x space 10 to the power of 23 over denominator 0.027 end fraction space equals 4$

Since the number of atoms in the unit cell is four, the given cubic unit cell has a face-centred cubic (fcc) or cubic-closed packed (ccp) structure.

Some More Questions From The Solid State Chapter

Why do solids have a definite volume?

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.

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The Solid State

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?

Some More Questions From The Solid State Chapter

Why do solids have a definite volume?

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.

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For Daily Free Study Material Join wiredfaculty

The Solid State

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?

Some More Questions From The Solid State Chapter

Why do solids have a definite volume?

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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?

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.