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Q.

Lattice energy of NaCl is 'X'. If the ionic size of A+2 is equal to that of Na+ and B–2 is equal to Cl, then lattice energy associated with the crystal AB is

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a

4X

b

2X

c

8X

d

X

answer is C.

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Detailed Solution

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Lattice energy \large U\propto \frac{{{Z}^{+}}{{Z}^{-}}}{{{r}_{+}}+{{r}_{-}}}

Given ionic size of Na+ = A+2

Given ionic size of Cl- = B-2

thus inter ionic distance \large \left( {{r}_{+}}+{{r}_{-}} \right) remains constant

\large \therefore U\propto {{Z}^{+}}{{Z}^{-}}

\large \Rightarrow \frac{{{U}_{NaCl}}}{{{U}_{AB}}}=\frac{\left( 1 \right)\left( 1 \right)}{\left( 2 \right)\left( 2 \right)}

\large {{U}_{AB}}=4{{U}_{NaCl}}

\large {{U}_{AB}}=4X\left( X={{U}_{NaCl}} \right)

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