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KVPY Sample Paper KVPY Stream-SX Model Paper-7

  • question_answer
    The face diagonal length of f.c.c. cubic cell is \[660\sqrt{2}\text{ }pm\]. If the radius of the cation is 110 pm. the radius of the anion is

    A) 249pm                         

    B)  220pm        

    C) 608pm                         

    D) 176pm

    Correct Answer: B

    Solution :

    \[\sqrt{2}a=660\sqrt{2}\,pm\]
    So \[a=660\,pm\]
    Now if tetrahedral void is occupied by cations than
    \[\frac{\sqrt{3}}{4}a=({{r}_{+}}+{{r}_{-}})\,;{{r}_{-}}=\left( \frac{\sqrt{3}+600}{4}-110 \right)\]\[=110\left[ \frac{3}{2}\sqrt{3}-1 \right]=1.598\times 110\]
    So \[\frac{{{r}_{+}}}{{{r}_{-}}}=\frac{1}{1.598}=\frac{1}{1.6}=\frac{10}{16}=0.625\]
    But \[\frac{{{r}_{+}}}{{{r}_{-}}}>0.414\]so it must not be occupying tetrahedral void then
    \[a=2({{r}_{+}}+{{r}_{-}})\]   \[\Rightarrow \]   \[330={{r}_{+}}+{{r}_{-}}\]
    \[{{r}_{-}}=220\,pm\]
    {\[\frac{{{r}_{+}}}{{{r}_{-}}}=0.5\]it can occupy octahedral void}


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