If packing fraction of two dimension unit cell shown in figure is A, then calculate value of 1000 A.

$\text{ [Take }\pi =3.2,\sqrt{2}=1.4\text{ ] }$

Fill your answer as sum of digits (excluding decimal places) till you get the single digit answe.

packing fraction = area occupid by sphere Total crea

AB=H=L2+L2=2L2=2LH=2L

In the form of circle = 4r

2L=4rr=2L4

Area of squre L2=42r2=162r2=8r2

Area of squre = 8r2

Total area occupied of circle =I+14×4(Il)

Area of circle = πr2

a2=4R

Area available = a2

Area occupied = 2πR2

packing fraction = 2πr28r2−28π=π4=3.144

A=0.785