An element crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 10²³ atoms.

Solution

Solution:
We have given that
Edge length of the unit cell
= 200 pm = 200 x 10^–10 cm

Vol. of the unit cell
= (200 x 10^–10 cm)³= 8 x 10^–24 cm³Therefore, volume of the substance
= Vol. of unit cell x Vol. of 1 unit cell.

Since the element has a fcc unit cell, number of atoms per unit cell = 4.
Total number of atoms = Atoms/unit cell x number of unit cells.
= 24 x 10²³atoms = 4

atoms/unit cell x No. of unit cells.

∴ No. of unit cells = $\frac{24 \times 10^{23} atoms}{4 atoms / unit cell}$

$= 6 \times 10^{23} unit cells .$

∴ Volume of the substance
$6 \times 10^{23} unit cell \times 8 \times 10^{- 24} {cm}^{3} / unit cell = 4.8 {cm}^{3}$

Now, $Density = \frac{Mass}{Volume} = \frac{200 g}{4.8 {cm}^{3}} = 4.17 g {cm}^{- 3} .$

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The Solid State

An element crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 10²³ atoms.

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 crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 1023 atoms.

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 crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 10²³ atoms.

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.