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Solid State

Section: Chemistry

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Question : 14 of 19

Marks: +1, -0

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

[JEE Adv 2010 P2]

39.27%
68.02%
74.05%
78.54%

Solution:

If R is the radius of the atom, then for the given unit cell,

a = L =

(2\sqrt{2}R)

Then area of the square unit cell is

L × L =

(2\sqrt{2}R)^2

=

8R^2

Area of atoms present in one unit cell is

\pi R^2 + 4\left(\frac{\pi R^2}{4}\right)

=

2\pi R^2

Therefore, packing efficiency is

\frac{2\pi R^2}{8R^2}

× 100 =

\frac{\pi}{4} \times 100

= 78.54 %

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