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(C) Step $1$: Convert the edge length $a$ from $	ext{pm}$ to $	ext{cm}$.$a = 500 	ext{ pm} = 500 	imes 10^{-10} 	ext{ cm} = 5 	imes 10^{-8} 	ex

Vedclass · Accepted Answer

$8.0 	imes 10^{21}$

Vedclass · Answer

(C) Step $1$: Convert the edge length $a$ from $	ext{pm}$ to $	ext{cm}$.$a = 500 	ext{ pm} = 500 	imes 10^{-10} 	ext{ cm} = 5 	imes 10^{-8} 	ext{ cm}$.Step $2$: Calculate the volume of one unit cell $(V_{uc} = a^3)$.$V_{uc} = (5 	imes 10^{-8} 	ext{ cm})^3 = 125 	imes 10^{-24} 	ext{ cm}^3 = 1.25 	imes 10^{-22} 	ext{ cm}^3$.Step $3$: Calculate the number of unit cells in $1 	ext{ cm}^3$.$	ext{Number of unit cells} = \frac{	ext{Total volume}}{	ext{Volume of one unit cell}} = \frac{1 	ext{ cm}^3}{1.25 	imes 10^{-22} 	ext{ cm}^3} = 0.8 	imes 10^{22} = 8.0 	imes 10^{21}$.

Calculate the number of unit cells in $1 \text{ cm}^3$ of metal if it forms a simple cubic structure with a unit cell edge length of $500 \text{ pm}$.

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