1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

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 'r'.

The volume of this HCP unit cell is :

A
$$24\sqrt 2 \,{r^3}$$
B
$$16\sqrt 2 \,{r^3}$$
C
$$12\sqrt 2 \,{r^3}$$
D
$${{64} \over {3\sqrt 3 }}\,{r^3}$$
2
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

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 'r'.

The empty space in this HCP unit cell is :

A
74%
B
47.6%
C
32%
D
26%
3
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-0

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Column I Column II
(A) Simple cubic and face-centred cubic (P) have these cell parameters $$a=b=c$$ and $$\alpha=\beta=\gamma$$
(B) cubic and rhombohedral (Q) are two crystal systems
(C) cubic and tetragonal (R) have only two crystallographic of 90$$^\circ$$
(D) hexagonal and monoclinic (S) belong to same crystal system

A
$$\mathrm{A-(s);B-(q);C-(q);(d)-(q,r)}$$
B
$$\mathrm{A-(p,s);B-(p);C-(q);(d)-(r)}$$
C
$$\mathrm{A-(p,s);B-(p,q);C-(q);(d)-(q,r)}$$
D
$$\mathrm{A-(s);B-(q);C-(q);(d)-(q)}$$

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