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The packing efficiency of a two-dimensional square unit cell shown below is
image
A. `32.97%`
B. `68.02%`
C. `74.05%`
D. `78.54%`

1 Answer

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Correct Answer - D
Number of particles in one unit cell
`=1+4xx(1)/(4)=2`
If radius of particle is `r` then total are a covered by particles `=2pir^(2)`
Total area of unit cell `=L^(2)(or a^(2))`
Bur`,a=2sqrt(2)r`
and Packing efficiency `=("Area covered by particle")/("Total area")=(2pir^(2))/((2sqrt(2))^(2))=(pi)/(4)`
`implies (22)/(7xx4)xx100=78.54%`
image

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