The Solid State

Question 149

If NaCl is doped with 10–3 mol % of SrCl2' what is the concentration of cation vacancies?


We know that two Na+ ions are replaced by each of the Sr2+ ions while SrCl2 is doped with NaCl. But in this case, only one lattice point is occupied by each of the Sr2+ ions and produce one cation vacancy.

Here 10 – 3 mole of SrCl2 is doped with 100 moles of NaCl Thus, cation vacancies produced by NaCl = 10 – 3 mol Since, 100 moles of NaCl produces cation vacancies after doping = 10 –3 mol

Therefore, 1 mole of NaCl will produce cation vacancies after doping
10 to the power of negative 3 end exponent over 100 space equals 10 to the power of negative 5 end exponent space mol
therefore, total cationic vacancies
=10-5 x Avogadro's number
=10-5  x 6.023 x 1023
=6.023 x 10-18 vacancies

Question 150

The ionic radius of CI ion is 181 pm. Consider the closest packed structure in which all anions are just touching:
(i) Calculate the radius of the cation that just fits into the octahedral holes of this lattice of anions. (ii) Calculate the radius of the cation that just fits into the tetrahedral holes of this lattice of anions.

Radius = 181 pm
Radius of octahedral void = 0.414 r = 0.414 x 181 pm = 74.934 pm
Cation having radius 74.934 pm will just fit into octahedral voids.

Radius of tetrahedral void

= 0.225 r = 0.225 x 181 pm = 40.725 pm
Cation having radius 40.725 pm will just fit into tetrahedral void.
Question 151

An element occurs in BCC structure with cell edge of 300 pm. The density of the element is 5.2 g cm–3. How many atoms of the element does 200 g of the element contain?

we have given that
z = 2 
a = 300 pm
d = 5.2 gm cm
by using the given formula we obtaine mass of element i.e.           
Question 152

Iron (II) oxide has a cubic structure and each unit cell has side 5A. If the density of the oxide is 4 g cm–3, calculate the number of Fe2+ and O2– ions present in each unit cell. (Molar mass of FeO = 72 g mol–1, NA = 6.02 x 1023 mol–1).


We  have given
volume of the unit cell = (5 x 10-8cm)3 = 1.25 x 10-22cm3

Density of FeO = 4g cm-3


ρ = z×Ma3×NA4= z×72(5×10-8)3×6.02×1023z= 4×1.25×10-22 ×6.02×102372 = 4.18 4

Each unit cell has four units of FeO. So it has four Fe2+ and four O2– ions.

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