Question
What is packing efficiency? Determine the packing efficiency of hcp and ccp structure.
✓
Answer
Packing Efficiency : Percentage of the avai-lable volume occupied by the ispheres (atoms) is called packing efficiency.
Packing Efficiency in hep and cep structures.
In cep and hep structures the packing efficiency is 74%. Let us calculate the packing efficiency in ccp structure.
In figure, let the unit cell edge length by 'a' and face diagonal. AC = b.
In $\Delta ABC$,$\quad$$AC ^2= BC ^2+ AB ^2$
$b^2=a^2+a^2 \Rightarrow b=\sqrt{2} a$
If $r$ is the radius of sphere, then
$b=4 r=\sqrt{2} a \Rightarrow a=\frac{4 r}{\sqrt{2}}=2 \sqrt{2} r ; \therefore r=\frac{a}{2 \sqrt{2}}$
There are four spheres per unit cell in ccp structure.
Volume of four spheres $=4 \times \frac{4}{3} \pi r^3$, and
Volume of cubic is $a^3=(2 \sqrt{2} r)^3=16$
Percentage of packing efficiency
$=\frac{\text { Volume occupied by four spheres of unit cell }}{\text { Total Volume of the Unit Cell }} \times 100 \%$
$=\frac{4 \times \frac{4}{3} \pi r^3 \times 100}{16 \sqrt{2} \pi^3} \%=\frac{\pi}{3 \sqrt{2}} \times 100 \%=74 \%$
Packing Efficiency in hep and cep structures.
In cep and hep structures the packing efficiency is 74%. Let us calculate the packing efficiency in ccp structure.
In figure, let the unit cell edge length by 'a' and face diagonal. AC = b.
In $\Delta ABC$,$\quad$$AC ^2= BC ^2+ AB ^2$
$b^2=a^2+a^2 \Rightarrow b=\sqrt{2} a$
If $r$ is the radius of sphere, then
$b=4 r=\sqrt{2} a \Rightarrow a=\frac{4 r}{\sqrt{2}}=2 \sqrt{2} r ; \therefore r=\frac{a}{2 \sqrt{2}}$
There are four spheres per unit cell in ccp structure.
Volume of four spheres $=4 \times \frac{4}{3} \pi r^3$, and
Volume of cubic is $a^3=(2 \sqrt{2} r)^3=16$
Percentage of packing efficiency
$=\frac{\text { Volume occupied by four spheres of unit cell }}{\text { Total Volume of the Unit Cell }} \times 100 \%$
$=\frac{4 \times \frac{4}{3} \pi r^3 \times 100}{16 \sqrt{2} \pi^3} \%=\frac{\pi}{3 \sqrt{2}} \times 100 \%=74 \%$
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Match the complex species given in Column $I$ with the possible isomerism given in Column $II$ and assign the correct code:
Code:
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Column $I ($Complex species$)$
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Column $II ($Isomerism$)$
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| $a.$ | $[Co(NH_3)_4C_{l2}]^+$ | $1.$ |
Optical
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| $b.$ | $cis-[Co(en)_2Cl_2]^+$ | $2.$ |
Ionisation
|
| $c.$ | $[Co(NH_3)_5 (NO_2)]Cl_2$ | $3.$ |
Coordination
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| $d.$ | $[Co(NH_3)_6][Cr(CN)_6]$ | $4.$ |
Geometrical
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| $5.$ |
Linkage
|
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