What is the molar mass of a metal having a de | vedclass

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(B) The packing efficiency of $68 \%$ corresponds to a Body-Centered Cubic $(BCC)$ unit cell.For a $BCC$ unit cell,the number of atoms per unit cell i

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$93 \ g \ mol^{-1}$

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(B) The packing efficiency of $68 \%$ corresponds to a Body-Centered Cubic $(BCC)$ unit cell.For a $BCC$ unit cell,the number of atoms per unit cell is $Z = 2$.The edge length $a = 3.3 \ \mathring{A} = 3.3 	imes 10^{-8} \ cm$.The density formula is given by $d = \frac{Z \cdot M}{N_A \cdot a^3}$,where $N_A = 6.022 	imes 10^{23} \ mol^{-1}$.Rearranging for molar mass $M$: $M = \frac{d \cdot N_A \cdot a^3}{Z}$.Substituting the values: $M = \frac{8.57 	imes 6.022 	imes 10^{23} 	imes (3.3 	imes 10^{-8})^3}{2}$.$M = \frac{8.57 	imes 6.022 	imes 10^{23} 	imes 35.937 	imes 10^{-24}}{2}$.$M = \frac{185.48}{2} \approx 92.74 \ g \ mol^{-1}$.Rounding to the nearest integer,$M = 93 \ g \ mol^{-1}$.

What is the molar mass of a metal having a density of $8.57 \ g \ cm^{-3}$ and an edge length of $3.3 \ \mathring{A}$? (Packing efficiency $= 68 \%$)

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