Solid State - Result Question 16

####16. The arrangement of $X^{-}$ions around $A^{+}$ion in solid $A X$ is given in the figure (not drawn to scale). If the radius of $X^{-}$is $250 pm$, the radius of $A^{+}$is

(2013 Adv.)

(a) $104 pm$

(b) $125 pm$

(c) $183 pm$

(d) $57 pm$

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Answer:

Correct Answer: 16. (a)

Solution:

  1. PLAN Given arrangement represents octahedral void and for this

$$ \begin{aligned} & \frac{r _{+} \text {(cation) }}{r _{-} \text {(anion) }}=0.414 \\ \frac{r\left(A^{+}\right)}{r\left(X^{-}\right)} & =0.414 \\ r\left(A^{+}\right) & =0.414 \times r\left(X^{-}\right)=0.414 \times 250 pm \\ & =103.5 pm \approx 104 pm \end{aligned} $$



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