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The density of copper metal is $8.95 g {cm}^{- 3}$ . If the radius of copper atom be $127.8 pm$ , is the copper unit cell simple cubic, body-centred cubic or face-centred cubic? (Given: atomic mass of $Cu = 63.54 g {mol}^{- 1} and NA = 6.02 \times 10^{23} {mol}^{- 1}$ )

Important Questions on Solid State

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

If 'a' stands for the edge length of the cubic system: simple cubic, body-centred cubic and face-centred cubic, the ratio of radii of the spheres in these systems will be respectively

HARD

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

Consider the bcc unit cells of the solids $1$ and $2$ with the position of atoms as shown below. The radius of atom $B$ is twice that of atom $A .$ The unit cell edge length is $50 %$ more in solid $2$ than in $1$ . What is the approximate packing efficiency in solid $2$ ?

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

The percentage of unoccupied volume in simple cubic cell is

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Chemistry>Physical Chemistry>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)

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Chemistry>Physical Chemistry>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]

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

The correct order of the packing efficiency in different types of unit cells is

EASY

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

a

the length of the side of a cube, the distance between the body centered atom one corner atom in the cube will be

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Chemistry>Physical Chemistry>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})

EASY

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

The vacant space in bcc lattice unit cell is:

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

A given metal crystallises out with a cubic structure having edge length of

361 pm

. If there are four metal atoms in one unit cell, what is the radius of one atom?

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

An element has a body centered cubic (bcc) structure with a cell edge of

288 pm

. The atomic radius is

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Chemistry>Physical Chemistry>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:

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Chemistry>Physical Chemistry>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>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}

)

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

A metal crystallises in face centred cubic structure with metallic radius

\sqrt{2} A °

. The volume of the unit cell (in

m^{3}

) is

EASY

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

The ratio of packing efficiency in

FCC, BCC

and simple cubic structure respectively, with respect to that of

FCC

structures is

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

Sodium crystallizes in bcc structure with radius

1.86 \times 10^{- 8} cm

. What is the edge length of unit cell of sodium?

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

A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is

' a'

, the closest approach between two atoms in the metallic crystal will be

HARD

Chemistry>Physical Chemistry>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})

EASY

Chemistry>Physical Chemistry>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?

The density of copper metal is 8.95 g cm–3. If the radius of copper atom be 127.8 pm, is the copper unit cell simple cubic, body-centred cubic or face-centred cubic? (Given: atomic mass of Cu = 63.54 g mol–1 and NA = 6.02 × 1023 mol–1)

Important Questions on Solid State

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The density of copper metal is $8.95 g {cm}^{- 3}$ . If the radius of copper atom be $127.8 pm$ , is the copper unit cell simple cubic, body-centred cubic or face-centred cubic? (Given: atomic mass of $Cu = 63.54 g {mol}^{- 1} and NA = 6.02 \times 10^{23} {mol}^{- 1}$ )