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← IIT-JEE 2008 · Paper 2
ChemistrySingle correct+4 / -1Question 63 of 66

IIT-JEE 2008 · Paper 2, Chemistry question 63

Passage

Paragraph for Question Nos. 61 to 63

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'rr'.

The empty space in this HCP unit cell is

Choose one option
Answer and worked solution

Official answer: D

Packing fraction.
6⋅43πr3242r3=π32≈0.74.\frac{6\cdot\frac43\pi r^3}{24\sqrt2r^3}=\frac{\pi}{3\sqrt2}\approx0.74.
So 26% of the cell is empty.

(D)