A) \[3.01\times {{10}^{23}}\]
B) \[6.02\times {{10}^{23}}\]
C) \[9.03\times {{10}^{23}}\]
D) \[12.04\times {{10}^{23}}\]
Correct Answer: A
Solution :
There are 12 edge centres. Contribution of \[N{{a}^{+}}\] ions at edge centres \[=12\times \frac{1}{4}=3\] Besides, there is one \[N{{a}^{+}}\] ion at body centre. Thus, there are four \[N{{a}^{+}}\] ions per unit cell. \[\frac{3}{4}\] are replaced by \[A{{l}^{3}}\] ions. Total \[N{{a}^{+}}\] ions in 1 mole of NaCl \[=6.023\times {{10}^{23}}\] \[N{{a}^{+}}\]ion replaced by \[A{{l}^{3+}}=3/4\times 6.023\times {{10}^{23}}\] \[1\,A{{l}^{3+}}\]replaces 3 \[N{{a}^{+}}\] ions thereby creating 2 vacancies. \[\therefore \]No. of vacancies created \[=\frac{2}{3}\times \left( \frac{3}{4}\times 6.023\times {{10}^{23}} \right)\] \[=3.01\times {{10}^{23}}\]
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