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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.

Solution:
we have given that
Density, d = 6.23 g/cm³
a = 400 pm
M = 60g/mol^-1
Volume = (a³)

= (400)^{3} = (400 \times 10^{- 10} cm)^{3}

Z = \frac{d \times a^{3} \times N_{A}}{M}

\frac{N_{A}}{M} = \frac{6.023 \times 10^{23} {mol}^{- 1}}{60 g / mol}

Z = \frac{6.023 g {cm}^{- 3} \times (400)^{3} \times 10^{- 30} {cm}^{3} \times 6.023 \times 10^{23} {mol}^{- 1}}{60 g {mol}^{- 1}} = \frac{6.023 \times 64 \times 6.023}{600} = \frac{2401.49}{600} = 4 .

Hence, the type of cubic unit cell is FCC

Radius = \frac{a}{a \sqrt{2}} = \frac{400}{2 \sqrt{2}} = \frac{200}{\sqrt{2}}

= \frac{200}{1.414} = 141.4 pm .

So radius of element is 141.4 pm

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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.

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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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