Question

167 Calculate packing the percentage efficiency of of Simple cubic cell. in case​

Answer 1

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• The percentage efficiency of packing in case of simple cubic cell is 52.4 %.

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In simple cubic unit cell, two atoms touch along the edge of the unit cell.

For simple cubic cell, the relationship between the edge length a and the radius r is a = 2r.

The volume of the unit cell V = a³ = (2r)³ = (8r³).

Each simple cubic cell contains eight atoms present at eight corners. Each atom contributes one eight to the unit cell. Hence, number of atoms present in one unit cell = 8 × 1/8 = 1.

The volume occupied by one atom in unit cell = 4/3πr³.

Packing efficiency = Volume occupied by one atom/Volume of cell unit × 100

• => 4/3πr³/8r³ × 100
• => Packing efficiency = 52.4%

Hence, the percentage efficiency of packing in case of simple cubic cell is 52.4 %.

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Answer 2

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In simple cubic unit cell, atoms are located at the corners of cube. Let us take a unit cell of edge length “a”. Radius of atom can be given as,

$r = \frac{a}{2}$

$a = 2r$

In simple cubic structures, each unit cell has only one atom,

$Packing \: \: efficiency = \begin{array}{l} \frac{volume~ occupied~ by~ one~ atom}{Total~ volume~ of~ unit ~cell}\end{array} \times 100$

$\frac{ (\frac{4}{3})\pi {r}^{3} \times 100 }{(2r)^{3} }$

$= 52.4\%$