The International Avogadro Coordination proje | vedclass

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Question

(C) The mass $m$ of the sphere is given by the volume of the sphere divided by the volume of the unit cell,multiplied by the number of atoms per unit

Vedclass · Accepted Answer

$1.2 	imes 10^{-8}$

Vedclass · Answer

(C) The mass $m$ of the sphere is given by the volume of the sphere divided by the volume of the unit cell,multiplied by the number of atoms per unit cell and the mass of one atom.$m = \frac{\frac{4}{3} \pi (d/2)^3}{a^3} 	imes 8 	imes \frac{M}{N_A}$Since $M$ and $N_A$ are constant,the relative error is given by:$\frac{\Delta m}{m} = 3 \frac{\Delta d}{d} + 3 \frac{\Delta a}{a}$Given $\Delta d = 0.2 \,nm = 0.2 	imes 10^{-9} \,m$ and $d = 9.4 \,cm = 9.4 	imes 10^{-2} \,m$.$\frac{\Delta d}{d} = \frac{0.2 	imes 10^{-9}}{9.4 	imes 10^{-2}} \approx 2.127 	imes 10^{-9}$.Given $\frac{\Delta a}{a} = 2 	imes 10^{-9}$.Substituting these values:$\frac{\Delta m}{m} = 3(2.127 	imes 10^{-9}) + 3(2 	imes 10^{-9})$$\frac{\Delta m}{m} = 6.381 	imes 10^{-9} + 6 	imes 10^{-9} = 12.381 	imes 10^{-9} \approx 1.2 	imes 10^{-8}$.

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