Element A has a face centred unit cell in which A is absent from half of the face centres. The packing fraction is x×√2π96.
The value of x is
A
3.33
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B
5
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C
7.45
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D
10
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Solution
The correct option is D 10 Contribution for a corner particle is =18 Contribution for a face centre particle is =12
Total no. of particles :
Zeff=(8×18)+(3×12)=52
For a FCC unit cell : Edge length(a)=2√2×r
Here r is the radius of particle A Total volumeV=a3=(2√2×r)3V=16√2×r3 Volume occupied(Vo)=Zeff×43×π×r3Vo=52×43×π×r3 Packing Fraction (P.F)=VoVP.F=52×43×π×r316√2×r3