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The Solid State

Short Answer Type

161. A metal (at. mass = 50) has a bcc crystal structure. The density of the metal is 5.96 g cm^–3. Find the volume of its unit cell?

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162. Calculate the density of silver which crystallizes in a face centred cubic lattice with unit cell length 0.4086 nm (At. mass of Ag = 107.88)

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Long Answer Type

163. An element crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 10²³ atoms.

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164. An element X with an atomic mass of 60 g/mol has density of 6.23 g/cm^–3. If the edge length of its cubic unit cell is 400 pm, identify the type of cubic unit cell. Calculate the radius of an atom of this element.

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Short Answer Type

165. An atom has fcc crystal whose density is 10 gm^–3 and cell edge is 100 pm. How many atoms are present in its 100 g?

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Long Answer Type

166. Analysis shows that a metal oxide has the empirical formula M_0.98 O_1.00. Calculate the percentage of M²⁺ and M³⁺ ions in this crystal.

Or

In an ionic compound the anion (N) form cubic close type of packing. While the cation (M⁺) ions occupy one third of the tetrahedal voids. Deduce the empirical formula of the compound and the coordination number of (M) ions.

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167. An element E crystallizes in body centred cubic structure. If the edge length of the cell is 1.469 x 10^–10 m and the density is 19.3 g cm^–3, calculate the atomic mass of this element. Also calculate the radius of this element.

Solution:
We have given that
Z= 2 since it is bcc structure
edge length, a = 1.469 x 10^-10
Density, d= 19.3 g cm^-3Mass = ?

d = \frac{2 \times 3}{a^{3} \times N_{A}} 19.3 = \frac{2 \times M}{(1.469 \times 10^{- 8})^{3} \times 6.023 \times 10^{23}} or M = \frac{19.3 \times 3.17 \times 10^{- 34} \times 6.023 \times 10^{23}}{2} = \frac{19.3 \times 3.17 \times 6.023 \times 10}{2} = 18.4 g {mol}^{- 1} .

mass of element is 18.4g mol^-1

(ii) Cell edge,

a = 1.469 \times 10^{- 10} m

Body diagonal = 4R

Then 4R =

\sqrt{39}

= \sqrt{3} \times 1.469 \times 10^{- 10} m

R = \frac{\sqrt{3} \times 1.469 \times 10^{- 10}}{4} m = 0.64 \times 10^{- 10} m = 6.4 \times 10^{- 11} m .

Radius of element is 6.4 x 10^-11m.

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168. Calculate the efficiency of packing in case of a metal crystal for
(i) simple cubic
(ii) body- centred cubic
(iii) face - centred cubic . (With the assumptions that atoms are touching each other).

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