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The Solid State

Question
CBSEENCH12005496
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Aluminium crystallizes in a cubic close-packed structure. Its metallic radius is 125 pm.
(a) What is the length of the side of the unit cell?
(b) How many unit cells are there in 1.00 cm3 of aluminium?

Solution

Given, radius of atom (r) = 125 pm
(a) For ccp structure, we know that,

straight r equals space fraction numerator straight a over denominator 2 square root of 2 end fraction where comma space straight r space equals space radius space and space straight a space equals space length space of space side space equals space 125 space pm space equals space fraction numerator straight a over denominator 2 square root of 2 end fraction straight a equals space 125 space straight x space 2 square root of 2 straight a equals 125 space straight x 2 space 1.414 space pm straight a equals 353.5 space pm left parenthesis straight b right parenthesis volume space of space 1 space unit space cell space equals straight a cubed equals left parenthesis 353.5 space straight x space 10 to the power of negative 3 end exponent cm right parenthesis cubed equals 44192902.36 space straight x 10 to the power of negative 30 end exponent space cm cubed equals 442 space straight x space 10 to the power of negative 25 end exponent space cm cubed Thus comma space number space of space unit space cell space of space aluminium space in space 1 space cm cubed equals fraction numerator 1 cm cubed over denominator 442 space straight x space 10 to the power of negative 25 end exponent space cm cubed end fraction equals 2.27 space straight x 10 to the power of 22 space unit space cell


 

Some More Questions From The Solid State Chapter

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.

Distinguish between Face-centred and end-centred unit cells.

What is the two-dimensional coordination number of a molecule in square close packed layer ?

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