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JEE MainChemistrySolid State

A metal initially crystallizes in a face-centred cubic (fcc) lattice with an edge length of 400 pm . Upon cooling, it undergoes a phase transition to a simple cubic (sc) lattice with an edge length of 200 pm . However, the sc lattice is non-ideal and contains Schottky defects (missing atoms). If the ratio of the density of the fcc lattice to the measured density of the defective sc lattice is 25 48 , the percentage o

Correct answer

4

Step-by-step solution

The density of a crystal lattice is given by: d = Z M N_A a^3 Taking the ratio of the densities of the fcc lattice and the defective sc lattice: d_ fcc d_ sc = ( Z_ fcc Z_ sc(eff) ) ( a_ sc a_ fcc )^3 Given data: Z_ fcc = 4 a_ fcc = 400 pm a_ sc = 200 pm d_ fcc d_ sc = 25 48 Substituting these values into the ratio equation: 25 48 = ( 4 Z_ sc(eff) ) ( 200 400 )^3 25 48 = 4 Z_ sc(eff) ( 1 2 )^3 25 48 = 4 Z_ sc(eff) 1 8 25 48 = 1 2 Z_ sc(eff) 2 Z_ sc(eff) = 48 25 Z_ sc(eff) = 24 25 = 0.96 For an ideal simple cubic la

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