A metal crystallizes in a simple cubic unit c | vedclass

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(A) $1$. The volume of the unit cell $V_{cell} = a^3 = (3.36 	imes 10^{-8} 	ext{ cm})^3 = 37.933 	imes 10^{-24} 	ext{ cm}^3 = 3.7933 	imes 10^{-2

Vedclass · Accepted Answer

$1.807 	imes 10^{-23} 	ext{ cm}^3$

Vedclass · Answer

(A) $1$. The volume of the unit cell $V_{cell} = a^3 = (3.36 	imes 10^{-8} 	ext{ cm})^3 = 37.933 	imes 10^{-24} 	ext{ cm}^3 = 3.7933 	imes 10^{-23} 	ext{ cm}^3$.$2$. For a simple cubic unit cell, the packing efficiency is $\frac{\pi}{6} \approx 0.524$.$3$. The occupied volume $V_{occ} = 0.524 	imes V_{cell} = 0.524 	imes 3.7933 	imes 10^{-23} 	ext{ cm}^3 \approx 1.987 	imes 10^{-23} 	ext{ cm}^3$.$4$. The void volume $V_{void} = V_{cell} - V_{occ} = V_{cell} 	imes (1 - 0.524) = 3.7933 	imes 10^{-23} 	imes 0.476 \approx 1.8056 	imes 10^{-23} 	ext{ cm}^3$.$5$. The closest value is $1.807 	imes 10^{-23} 	ext{ cm}^3$.

$A$ metal crystallizes in a simple cubic unit cell. Calculate the void volume of the unit cell. $[a = 3.36 \times 10^{-8} \text{ cm}]$

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