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Question

In which of the following most efficient packing at present?


A

hcp

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B

bcc

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C

Simple cubic

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D

None Of These

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Solution

The correct option is A

hcp


The explanation for the correct answer

Correct Answer: Option (A) HCP

Packing fraction

  • Packing efficiency or packing fraction is the fraction of volume occupied by a constituent particle in a crystal structure.
  • It is a dimensionless quantity and always less than unity.

HCP or hexagonal closed packing

HCP has 6 atoms per unit cell,

Lattice constant a = 2r

Packing fraction= NAtomsVAtomsVUnitcell

6×4/3πr333/2×(2r2)×(2/3×4r=0.74(orc/aratio=1.633),

Atomic Packing Factor APF = 74%.

Hence, option a is correct.

The explanation for incorrect answers

(B) BCC has a packing fraction of 68%. Hence, option (B) is incorrect.

(C) simple Cubic has a packing fraction of 52%. Hence, option (C) is incorrect.

(D) Option(D) does not hold.


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