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Select right expression for determinig ...

Select right expression for determinig packing fraction (P.F.) of NaCl unit cell (assume ideal ) , if ions along an edge diagonal are absent :

A

`P.F = ((4)/(3) pi(r_(+)^(3) + r_(-)^(3)))/(16sqrt2 r^(3))`

B

`P.F = ((4)/(3) pi [(5)/(2) r_(+)^(3) + r_(-)^(3)])/(16 sqrt2 r_(-)^(3))`

C

`P.F = ((4)/(3) pi [(5)/(2) r_(+)^(3) + r_(-)^(3)])/(16 sqrt2 r_(-)^(3))`

D

`P.F = ((4)/(3) pi [(7)/(2) r_(+)^(3) + r_(-)^(3)])/(16 sqrt2 r_(-)^(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
Effective no. of `Na^(+)=4-(1+2xx(1)/(4))=(5)/(2)`
Effective no. of `Cl^(-)=4sqrt(2)a=4r^(-)`
P.F, `=("Vol. of effective no. of cations and anions")/("Vol. of unit cell")`
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