Solid State MCQ Questions & Answers in Physical Chemistry | Chemistry

$$\eqalign{ & {\text{No}}{\text{.}}\,{\text{of}}\,{\text{spheres}}\,{\text{in}}\,fcc \cr & = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} \cr & = 4 \cr & {\text{Volume}}\,{\text{of}}\,{\text{4}}\,{\text{spheres}} \cr & = 4 \times \frac{4}{3}\pi {r^3} \cr & = \frac{{16}}{3}\pi {r^3} \cr} $$

$$hcp$$  is a closed packed arrangement in which the unit cell is hexagonal and coordination number is 12.

From the given data, we have
Number of $$Y$$ atoms in a unit cell = 4
Number of $$X$$ atoms in a unit cell $$ = 8 \times \frac{2}{3} = \frac{{16}}{3}$$
From the above we get the formula of the compound as
$${X_{\frac{{16}}{3}}}\,{Y_4}\,\,or\,\,{X_4}{Y_3}$$

Potassium crystallises in $$bcc$$  lattice.

Frenkel defect is shown by ionic solids. The smaller ion ( usually cation ) is dislocated from its lattice site to interstitial site.

At sufficiently low temperature, the thermal energy is low and intermolecular forces bring the particles so close that they cling to one another and occupy fixed positions. The particles can still oscillate about their mean positions and the substance exists in solid state.

The arrangement given shows octahedral void arrangement-limiting radius ratio for octahedral void is
$$\eqalign{ & \frac{{{r_{{A^ + }}}}}{{{r_{{X^ - }}}}} = 0.414 \cr & {r_{{A^ + }}} = 0.414 \times {r_{{X^ - }}} = 0.414 \times 250 = 103.5 \approx 104pm. \cr} $$

When third layer is placed over the second layer and all tetrahedral voids are covered by the spheres of the third layer then in this case, the spheres of the third layer are exactly aligned with those of the first layer. $$\left( {ABAB....{\text{pattern}}} \right).$$    This structure is called hexagonal close packed $$(hcp)$$  structure.

No. of M atoms $$ = \frac{1}{4} \times 4 + 1 = 1 + 1 = 2$$
No. of X atoms $$ = \frac{1}{2} \times 6 + \frac{1}{8} \times 8 = 3 + 1 = 4$$
So, formula = $${M_2}{X_4} = M{X_2}$$

The amount of energy released when cation and anions are brought from infinity to their respective sites in the crystal lattice to form one mole of the ionic compounds is called the lattice energy. $$N{a^ + }$$  being smallest in size have highest lattice energy.