JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Solid State

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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 centered cations (M) by anions (X)
(iii) Remove all the corner cations (M)
(iv) Replace the central anion (X) with cation (M)

The value of

(\frac{number of anions}{number of cations})

Z

is ____.

Answer: 3

Solution

Starting with NaCl structure:

$M^{+}$ at corners (8 × 1/8 = 1) and face centers (6 × 1/2 = 3) → total 4 cations
$X^{-}$ at edge centers (12 × 1/4 = 3) and body center (1) → total 4 anions

Step (i): Remove all anions except the central one

$M^{+}$ : 4
$X^{-}$ : 1 (only body center)

Step (ii): Replace all face-centered cations by anions

$M^{+}$ : 4 - 3 = 1 (only corners remain)
$X^{-}$ : 1 + 3 = 4

Step (iii): Remove all corner cations

$M^{+}$ : 1 - 1 = 0
$X^{-}$ : 4

Step (iv): Replace the central anion with cation

$M^{+}$ : 0 + 1 = 1
$X^{-}$ : 4 - 1 = 3

Ratio =

\frac{number of anions}{number of cations} = \frac{3}{1} = 3

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer

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JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Solid State

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