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Question

In which of the following pair is most efficient packing is present?


A

hcp and ccp

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B

hcp and bcc

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C

bcc and ccp

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D

bcc and simple cubic cell

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Solution

The correct option is A

hcp and ccp


The explanation for the correct answer

Correct Answer: Option (A) HCP and CCP

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 and Cubic closed packing

HCP has 6 atoms per unit cell,

Lattice constant a = 2r

Packing fraction= NAtomsVAtomsVUnitcell

The volume of the unit cell for HCP is a hexagonal prism with an atom on each vertex, and 3 atoms in the centre.

VUnitcell=33/2×(2r2)×(2/3×4r)6×4/3πr333/2×(2r2)×(2/3×4r)=0.74(orc/aratio=1.633),

Atomic Packing Factor APF = 74%.

Simple Cubic Packing

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) is incorrect as the packing efficiency of BCC and SCP is less than HCP.


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