The packing efficiency of the two-dimensional square unit cell shown below is

Question

The packing efficiency of the two-dimensional square unit cell shown below is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/a43be0e2509fbdebdd5ddc9d0280aec1-.png" /> (A) 39.27 % (B) 68.02 % (C) 74.05 % (D) 78.54 %

Tardigrade Admin · Accepted Answer

Packing efficiency =( textArea covered by particle/ textTotal area) Let us assume radius of circle = r Edge length of square = a So, (2× π r2/a2) =(2π r2/(2√2r)2) =(π/4) ⇒ (π/4) × 100 =78.5 %

Q. The packing efficiency of the two-dimensional square unit cell shown below is

$39.27%$

$68.02%$

$74.05%$

$78.54%$

Packing efficiency $= \frac{Area covered by particle}{Total area}$
Let us assume radius of circle $= r$
Edge length of square $= a$
So, $\frac{2 \times π r ^{2}}{a ^{2}}$
$= \frac{2 π r ^{2}}{( 2 2 r ) ^{2}}$
$= \frac{π}{4}$
$\Rightarrow \frac{π}{4} \times 100$
$= 78.5%$

Q. The packing efficiency of the two-dimensional square unit cell shown below is

39.27%

68.02%

74.05%

78.54%

Packing efficiency =Total areaArea covered by particle​ Let us assume radius of circle =r Edge length of square =a So, a22×πr2​ =(22​r)22πr2​ =4π​ ⇒4π​×100 =78.5%

$39.27%$

$68.02%$

$74.05%$

$78.54%$

Packing efficiency $= \frac{Area covered by particle}{Total area}$
Let us assume radius of circle $= r$
Edge length of square $= a$
So, $\frac{2 \times π r ^{2}}{a ^{2}}$
$= \frac{2 π r ^{2}}{( 2 2 r ) ^{2}}$
$= \frac{π}{4}$
$\Rightarrow \frac{π}{4} \times 100$
$= 78.5%$