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The Solid State

Question
CBSEENCH12010420
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Calculate the packing efficiency of a metal crystal for a simple cubic lattice.

Solution

In a simple cubic lattice, the particles are located only at the corners of the cube and touch each other along the edge.

In a simple cubic lattice, the particles are located only at the corners of the cube and touch each other along the edge.

Let the edge length of the cube be ‘a’ and the radius of each particle be r.

So, we can write:

a = 2r

Now, volume of the cubic unit cell = a3 = (2r)3 = 8r3

We know that the number of particles per unit cell is 1.

Therefore, volume of the occupied unit cell =  4 over 3 pi r cubed
Hence comma space packing space efficiency space equals space fraction numerator Volume space of space one space particle over denominator Volume space of space cubic space unit space cell end fraction space straight x space 100 percent sign space equals space fraction numerator begin display style 4 over 3 end style πr cubed over denominator 8 straight r cubed end fraction space straight x space 100 percent sign equals 1 over 6 straight pi space straight x space 100 percent sign equals 1 over 6 space straight x 22 over 7 space straight x 100 percent sign space equals 52.4 percent sign

Some More Questions From The Solid State Chapter

Why are solids rigid?

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'.

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