Question

Consider an 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 ........

Answer 1

Correct Answer - `3.00`
According to the given information , cations are present on the corners and face centres and anions are present on the edge centres and body centre. In MX, their contributions towards the unit cell are as under :
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