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Consideran ionic solid MX with NaCl structure . Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance . (i)Remove all the anions (X) except the central one. (ii)Replace all the face-centred cations (M) by anions (X) (iii)Remove all the corner cations (M) (iv)Replace the central anion (X) with cation (M) The value of ("number of anions"/"number of cations") in Z is ........ |
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Answer» Anions `(X^-)=UNDERSET"(edge centres)"(12xx1/4)+underset"(body centre)"(1)=3+1=4` Cations`(M^+)`=`underset"(corners)"(8xx1/8)+underset"(face centres)"(6xx1/2)=1+3=4` After step (i), anions `(X^-)` LEFT =4-3=1 After step (ii), cations `(M^+)` left=4-3=1 anions `(X^-)`=1+3=4 After step(iii), cations `(M^+)` left =1-1=0 After step (iv), anions `(X^-)` left =4-1=3, cations `(M^+`) =0+1=1 Hence ratio `"NUMBER of anions "/"number of cations"` in Z=`3/1`=3 Alternatively, Anions `(X^-)=underset"edge centres""12"+underset"body centre""1"` Cations `(M^+)=underset"corners""8"+underset"face centres""6"` After step (i), anions `(X^-)` = `underset"body centre"1` , cations `(M^+)= underset"corners""8"+underset"face centres"6` After step (ii) ,anions `(X^-)=underset"body centre"1 + underset"face centres"6, cations `(M^+)=underset"corners""8"+underset"face-centre"0` After step (iii), anions `(X^-)=underset"body centre"1+underset"face centres"6` , cations `(M^+)=underset"corner"0+underset"face centre"0` After step (iv), anions `(X^-)=underset"body centre"0+underset"face centres"6`, cations `(M^+)=underset"body centre"1` As anion at the face centre has contribution =`1/2` towards the unit cell `therefore` Anions `(X^-)` PER unit cell in Z =`6xx1/2=3` As cation at the body centre has contribution =1 `therefore` Cations `(M^+)` per unit cell in Z=1 `therefore` Ratio `"number of anions"/"number of cations "` in Z =`3/1`=3 |
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