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Elden [556K]
2 years ago
8

Iron has a mass of 7.87 g per cubic centimeter of volume, and the mass of an iron atom is 9.27 × 10-26 kg. If you simplify and t

reat each atom as a cube, (a) what is the average volume (in cubic meters) required for each iron atom and (b) what is the distance (in meters) between the centers of adjacent atoms?
Physics
1 answer:
Alecsey [184]2 years ago
4 0
Known values; mass per / volume and mass of each atom 

average volume=<span> volume per atom. </span>
<span>density*mass per atom = volume per atom </span>

<span>1cm^3 / 7.87 gram * 9.27 *10^-26 kg /atom* 1000 gram / kg=
</span>=<span>1.178 * 10^-22 cm^3 per atom </span>

<span>Convert that to mass </span>
<span>1 cm^3 * (1 m / 100 cm)^3 </span>
 average volume= <span>1.178 *10^-29 m^3 per  atom </span>

<span>distance: </span>

<span>Volume of a cube is L^3 </span>


<span>so L = (1.178*10^-29)^(1/3) </span>

<span>Half way through the cube is distance 1/2 L. </span>
<span>Second cube is 1/2 L </span>
<span>So distance between the center of 2 cubes = L </span>

=2.28 *10^-10 m 
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<u>Given:</u>

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\begin{aligned}&7.98 \times 10^{6}=\left(8.99 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right) \frac{48.8 \mathrm{C} \times 41.7 \mathrm{C}}{\mathrm{r}^{2}} \\&r=\sqrt{\frac{1.8294 \times 10^{13}}{7.98 \times 10^{6}}}=1.514  \times 10^{3} \mathrm{~m}=1.51 \mathrm{~km}\end{aligned}

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