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JEE Advanced levelNumerical answerDifficulty 3 of 3ss107

A NaCl crystal of volume $1.00 m m^{3}$ (edge of unit cell $564 pm$ , 4 anion sites per cell) has 1 in $1 0^{6}$ of its anion sites occupied by F-centres. Find the number of F-centres in units of $1 0^{13}$ (two decimals).

Numerical answer type, answer in x 10^13, tolerance 0.03.

Answer: 2.23 x 10^13

V = 1.00 m m^{3} = 1 0^{- 3} c m^{3}

and cell volume

= (5.64 \times 1 0^{- 8})^{3} = 1.794 \times 1 0^{- 22} c m^{3}

, giving

5.57 \times 1 0^{18}

cells. Anion sites

= 4 \times

cells

= 2.23 \times 1 0^{19}

. F-centres

= 2.23 \times 1 0^{19} \times 1 0^{- 6} = 2.2296 \times 1 0^{13} \approx 2.23 \times 1 0^{13}

.

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