A complex solid matrix contains elements P, Q, and R. Atoms of P form a Cubic Close Packed (CCP) lattice. Atoms of Q occupy exactly rd of the available tetrahedral voids. Atoms of R perfectly occupy e

Question

A complex solid matrix contains elements P, Q, and R. Atoms of P form a Cubic Close Packed (CCP) lattice. Atoms of Q occupy exactly $\frac{1}{3}$ rd of the available tetrahedral voids. Atoms of R perfectly occupy exactly $\frac{1}{2}$ of the available octahedral voids. If the empirical formula is deduced as $P_xQ_yR_z$, what is the minimum integer value for the sum $(x+y+z)$?

Prashant Kotian · Accepted Answer

Correct answer: 13. P forms CCP, so . There are 8 TVs; Q occupies . There are 4 OVs; R occupies . The stoichiometric ratio P : Q : R is . Multiplying by 3 gives , and simplifying yields . Thus, the empirical formula is . The sum .

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