# A pure copper sphere has a radius 0.929 in. How many copper atoms does it contain? (density of copper 8.96 "g/cm"^3)

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Jan 17, 2015

The answer is $4.67 \cdot {10}^{24}$ $\text{atoms}$.

So, start by converting inches to cm

$\text{0.929 cm" * ("2.54 cm")/("1 inch") = "2.360 cm}$

Use this value to determine the volume of the sphere

${V}_{\text{sphere}} = \frac{4}{3} \cdot \pi \cdot {r}^{3} = \frac{4}{3} \cdot 3.14 \cdot {2.360}^{3} = 55.03$ ${\text{cm}}^{3}$

Use density to determine the mass of copper

$\rho = \frac{m}{V} \implies m = \rho \cdot V = 8.96$ ${\text{g"/"cm}}^{3} \cdot 55.03$ ${\text{cm}}^{3} = 493$ $\text{g}$

From here, you can determine the number of atoms you have by

"493 g" * (6.022 * 10^23 "atoms")/("63.55 g") = 4.67 * 10^24 $\text{atoms}$

I've used the fact that 1 mole of copper has $6.022 \cdot {10}^{23}$ atoms and weighs $\text{63.55 g}$.

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