An element crystallizes in an f.c.c. structur | vedclass

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(C) Given: Edge length $(a) = 200 \, pm = 2 	imes 10^{-8} \, cm$.Volume of unit cell $(V) = a^3 = (2 	imes 10^{-8} \, cm)^3 = 8 	imes 10^{-24} \, c

Vedclass · Accepted Answer

$41.7$

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(C) Given: Edge length $(a) = 200 \, pm = 2 	imes 10^{-8} \, cm$.Volume of unit cell $(V) = a^3 = (2 	imes 10^{-8} \, cm)^3 = 8 	imes 10^{-24} \, cm^3$.Number of atoms per unit cell for $f.c.c.$ $(Z) = 4$.Mass of element $(m) = 200 \, g$.Total number of atoms $(N) = 24 	imes 10^{23}$.Density $(ho) = \frac{Z 	imes m}{V 	imes N}$.$ho = \frac{4 	imes 200 \, g}{8 	imes 10^{-24} \, cm^3 	imes 24 	imes 10^{23}}$.$ho = \frac{800}{8 	imes 24 	imes 10^{-1}} = \frac{800}{19.2} = 41.66 \approx 41.7 \, 	ext{g cm}^{-3}$.

An element crystallizes in an $f.c.c.$ structure with a unit cell edge length of $200 \, pm$. If $200 \, g$ of this element contains $24 \times 10^{23}$ atoms,calculate its density in $\text{g cm}^{-3}$.

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