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The edge length of unit cell of a metal ( $24$ molecular mass) having a cubic structure of $4.53 \overset{\circ}{A}$ . If the density of metal is $1.74 g / {cm}^{3}$ , what is the radius of this metal is? $(Average number = 6 \times 10^{23})$

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Important Questions on The Solid State

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

If same type of atoms are packed in hexagonal close packing and cubic close packing separately, then

HARD

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Lithium has a bcc structure. Its density is

530 k g m^{- 3}

and its atomic mass is

6.94 g m o l^{- 1}

. Calculated the edge length of a unit cell of Lithium metal.

(N_{A} = 6.02 \times 10^{23} m o l^{- 1})

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

A metal crystallizes in two phases, one as

fcc

and another as

bcc

with unit cell edge lengths of

3.5 \overset{°}{A}

and

3.0 \overset{°}{A}

, respectively. The ratio of density of

fcc

and

bcc

phases approximately is

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Calcium metal crystallizes in an f.c.c. lattice with edge length

0.556 nm

. If it contains

0.5 %

Frenkel defects, the density of the metal is

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

100^{o} C,

copper

(C u)

has

F C C

unit cell structure with cell edge length of

x Å

. What is the approximate density of

C u

(in

g c m^{- 3}

) at this temperature?

[A t o m i c M a s s o f C u = 63.55 u]

EASY

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

An element crystallises in fcc lattice. If edge length of the unit cell is

4.07 \times 10^{- 8} cm

and density is

10.5 g {cm}^{- 3} .

Calculate the atomic mass of element.

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Calculate the number of unit cells in

38.6 g

of noble metal having density

19.3 g {cm}^{- 3}

and volume of one unit cell is

6.18 \times 10^{- 23} {cm}^{3}

HARD

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Iron exhibits BCC structure at room temperature. Above

900^{°} C

, it transforms to FCC structure. The ratio of the density of iron at room temperature to that at

900^{°} C

is (assuming molar mass and atomic radii of iron remains constant with temperature)

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

A metallic element has a cubic lattice. Each edge of the unit cell is

2 \dot{A}

and the density of metal is

25 g {cm}^{3}

. The unit cell in

200 g

of metal are

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

The density of a solid

X

1.5 g / {cm}^{3}

250^{o} C

. If the atoms are assumed sphere of radius

2.0 A

, the percentage of solid having empty space is
(Given atomic weight of

X = 60 g {mol}^{- 1})

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

The edge length of a solid possessing cubic unit cell is $2 \sqrt{2} r$ (structure I), based on hard sphere model, which upon subjecting to a phase transition, a new cubic structure (structure II) having an edge length of $\frac{4 r}{\sqrt{3}}$ is obtained, where $r$ is the radius of the hard sphere. Which of the following statements is true ?

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

The number of atoms in

2.4 g

of body centred cubic crystal with edge length

200 pm

is (density

= 10 g {cm}^{- 3}, N_{A} = 6 \times 10^{23} atoms {mol}^{- 1}

)

EASY

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

A metal crystallises in BCC lattice with unit cell edge length of

300 pm

and density

6.15 {gcm}^{- 3} .

The molar mass of the metal is

EASY

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Copper crystallises with fcc unit cell. If the radius of copper atom is

127.8 pm,

calculate the density of copper? (at. Mass,

Cu = 63.55 g {mole}^{- 1}

)

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Copper crystallizes in an FCC unit cell with cell edge of

3 .608 \times 10^{- 8} cm .

The density of copper is

8.92 g / {cm}^{3}

, Calculate the atomic mass of copper.

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of

4.29 Å

. The radius of sodium atom is approximately:

EASY

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Iron crystallizes in several modifications. At about

911^{o} C

, the bcc

' α'

form undergoes a transition to fcc

' γ'

form. If the distance between two nearest neighbours is the same in the two forms at the transition temperature, what is the ratio of the density of iron in fcc form

(ρ_{2})

to the iron in bcc form

(ρ_{1})

at the transition temperature?

HARD

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

How many number of unit cells are present in

100 g

of an element with FCC crystal having density

10 g / {cm}^{3}

and edge length

100 pm

MEDIUM

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

A diatomic molecule

X_{2}

has a body-centred cubic

(bcc)

structure with a cell edge of

300 pm .

The density of the molecule is

6.17 {gcm}^{- 3} .

The number of molecules present in

200 g

X_{2}

is :
(Avogadro constant

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

)

EASY

Chemistry>Physical Chemistry>The Solid State>Calculations Involving Unit Cell Dimensions

Copper

(A t o m i c m a s s = 63.5)

crystallizes in a FCC lattice and has density

8 .93 g . {cm}^{- 3} .

The radius of copper atom is closest to

The edge length of unit cell of a metal (24 molecular mass) having a cubic structure of 4.53 A∘. If the density of metal is 1.74 g/cm3, what is the radius of this metal is? Average number =6×1023

Important Questions on The Solid State

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The edge length of unit cell of a metal ( $24$ molecular mass) having a cubic structure of $4.53 \overset{\circ}{A}$ . If the density of metal is $1.74 g / {cm}^{3}$ , what is the radius of this metal is? $(Average number = 6 \times 10^{23})$