SATHEE: Solid State - Result Question 45

Solid State - Result Question 45

####45. A metallic element crystallises into a lattice containing a sequence of layers of $A B A B A B \dots .$ . Any packing of layers leaves out voids in the lattice. What percentage of this lattice is empty space?

(1996, 3M)

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Answer:

Correct Answer: 45. (0.74)

Solution:

The given arrangement : $A B A B A B \dots . .$ . represents hexagonal close-packed unit cell in which there are six atoms per unit cell. Also, volume of unit cell $= 24 \sqrt{2} r^{3}$ .

$\Rightarrow$ Packing fraction $= \frac{Volume occupied by atoms}{Volume of unit cell}$

$= 6 \times \frac{4}{3} π r^{3} \times \frac{1}{24 \sqrt{2} r^{3}} = 0.74$

$\Rightarrow$ Percent empty space $= 100 (1 - 0.74) = 26 \%$

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Solid State - Result Question 45

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