An element A crystallises in fcc structure. 200 g of this element has 4.12 × 10 24 atoms. The density of A is 7 .2 g cm - 3 . Calculate the edge length of the unit cell.

Given, density, ρ = 7 .2 g cm - 3 Since, it is given that 200 g of this element has 4 . 12 × 10 24 atoms, Molar mass, M = w × N A N = 200 × 6 . 023 × 10 23 4 . 12 × 10 24 = 29 . 23 g / mol The face-centred cubic structure has atoms located at each of the corners and the centres of all the cubic faces. Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. Therefore, effective number of atoms z in a face -centred cubic unit cell is four. By using the equation of density of cubic crystal system, ρ = z × M a 3 × N A a 3 = z × M ρ × N A a 3 = 4 × 29 . 23 7 .2 × 6 . 023 × 10 23 = 26 . 96 × 10 - 24 a = 2 .997 × 10 - 8 cm a = 299 .7 pm Hence, the edge length is 299 .7 pm .

Aluminium metal forms a cubic close-packed crystal structure. Its atomic radius is 125 × 10 - 12 m . Calculate the length of the side of the unit cell.

Cubic closed packing is another name given to face-centred cubic. Hexagonal closed packing and cubic closed packing are one of the forms in which a cubic lattice is arranged and face-centred cubic is one of the types of unit cells. In a cubic close packed structure, the length of the side of unit cell is related to radius by an equation, r = a 2 2 Or a = r × 2 2 Given, atomic radius r = 125 × 10 - 12 m = 125 × 10 - 10 cm = 125 pm . Putting the values in the equation, we get a = 125 × 2 × 1 .414 = 353 .5 pm .

Aluminium metal forms a cubic close-packed crystal structure. Its atomic radius is 125 × 10 - 12 m . How many such unit cells are there in 1 .00 m 3 of aluminium?

Cubic closed packing is another name given to face-centred cubic. Hexagonal closed packing and cubic closed packing are one of the forms in which a cubic lattice is arranged and face-centred cubic is one of the types of unit cells. In a cubic close packed structure, the length of the side of unit cell is related to radius by an equation, a = r × 2 2 Given, atomic radius r = 125 × 10 - 12 m = 125 × 10 - 10 cm = 125 pm . Putting the values in the equation, we get a = 125 × 2 × 1 .414 = 353 .5 pm . Volume of the unit cell = ( a 3 ) = 353.5 × 10 - 10 3 = 4.42 × 10 - 23 cm 3 = 4 . 42 × 10 - 29 m 3 One unit cell contain the volume 4 . 42 × 10 - 29 m 3 Number of unit cells are present in 1 m 3 = ? Number of unit cells in 1 m 3 = 1 4 . 42 × 10 - 29 = 2 .26 × 10 28 unit cells.

ZnO turns yellow on heating. Why?

In ZnO , Zn + 2 ions occupy the interstitial sites and electrons are trapped in the interstitial sites for neutralization. Crystals that show such type of defects are generally coloured. Zinc oxide is white in colour at room temperature. On heating, it loses oxygen and turns yellow.

E M B I B E

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 33

HARD

11th CBSE

IMPORTANT

Earn 100

A compound $AB$ crystallises in bcc lattice with the unit cell edge length of $380 pm$ . The distance between oppositely charged ions in the lattice is $329 pm$ . Calculate the radius of $B^{-}$ if the radius of $A^{+}$ is $190 pm$ .

Important Questions on States of Matter: Solid State

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 34

An element A crystallises in

fcc

structure.

200 g

of this element has

4.12 \times 10^{24}

atoms. The density of A is

7 .2 g {cm}^{- 3}

. Calculate the edge length of the unit cell.

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 35

A metal (atomic mass

= 50

) has a body centred cubic crystal structure. The density of the metal is

5 .91 {gcm}^{- 3}

. Find the volume of the unit cell

(N_{A} = 6 .023 \times 10^{23} atoms {mol}^{- 1})

.

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 36

Aluminium metal forms a cubic close-packed crystal structure. Its atomic radius is

125 \times 10^{- 12} m

. Calculate the length of the side of the unit cell.

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 36

Aluminium metal forms a cubic close-packed crystal structure. Its atomic radius is

125 \times 10^{- 12} m

. How many such unit cells are there in

1 .00 m^{3}

of aluminium?

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 37

A uni-univalent ionic crystal

AX

is composed of the following radii (arbitrary units) :

\begin{matrix} A^{+} & X^{-} \\ 1 .0 & 2 .0 \end{matrix}

Assuming that ions are hard spheres, predict giving reasons whether the crystal will have sodium chloride or cesium chloride structure. Calculate the volume of the unit cell.

HARD

11th CBSE

IMPORTANT

Pradeep's Chemistry Vol 1>Chapter 6 - States of Matter: Solid State>PROBLEMS FOR PRACTICE>Q 38

An element