If packing fraction of two dimension unit cell shown in figure is A, then calculate value of 1000 A. [Take π=3.2,2=1.4 ] Fill your answer as sum of digits (excluding decimal places) till you get the single digit answe.

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If packing fraction of two dimension unit cell shown in figure is A, then calculate value of 1000 A.
$[Take π = 3.2, \sqrt{2} = 1.4]$
Fill your answer as sum of digits (excluding decimal places) till you get the single digit answe.

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answer is 1.

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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

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