# Number of copper atoms in $1\mbox{cm}^3$ of copper

I'm starting my physics class and I'm really rusty on my conversions and stoichiometry,

The mass of a copper atom is $1.37\cdot 10^{-25}$ kg, and the density of copper is $8920 \mbox{kg/m}^3$.

I would ask this in physics.se, but the problem is more math based than anything.

So far, I've concluded that the Volume of a single copper atom is $(1.37 \cdot 10^{-25} \mbox{kg})/(8920 \mbox{kg/m}^3)$ ($\mbox{density} = \mbox{m/V}$, so $V = \mbox{m}/\mbox{density}) = 1.536\cdot 10^{-29}$ cubic meters

From here, I'm confused on how to calculate how many atoms are in 1 cubic meter. I know its probably something really simple that I'm just forgetting how to do.

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I think this should be on Chemistry SE. – Argon Jan 26 '13 at 23:56
Once you get your answer, don't forget that the question in the title is about cubic centimeters, not cubic meters. – Gerry Myerson Jan 26 '13 at 23:57
@Argon, I disagree. If you know the volume of a cell, and you want to know how many cells in a cubic centimeter, is that a biology problem? – Gerry Myerson Jan 26 '13 at 23:58
@Asaf, done.${}$ – Gerry Myerson Jan 26 '13 at 23:58

There are $(100)^3$ cubic centimetres in one cubic metre.

Thus the mass of a cubic cm of copper is $8920\times 10^{-6}$ kg. Divide this by the mass of an atom to find, approximately, the number of atoms.

Equivalently, first find the number of atoms in $1$ cubic metre, by dividing the mass by the mass of an atom. Then divide by $10^6$ to find the number of atoms in $1$ cubic centimetre.

As a check on your calculations, your final answer should be $6.51\times 10^{22}$ atoms. It would be unreasonable to give an answer to greater precision, since the mass of an atom is only given to us to $3$ significant figures.

Remark: Why divide? Suppose you know the mass $a$ of one apple, and you know that a bin full of apples has mass $B$. Then it is reasonably clear that there are $\dfrac{B}{a}$ apples in the bin. For if there are $n$ apples, then $an=B$. Solve for $n$.

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What you are missing is Avogadro's number. This is a chemistry question about Math, but the information is not commonly found in Math without Chemistry. http://education.jlab.org/qa/mathatom_03.html follow that link on the proper use of Avogadro's number (the number of atoms in a given unit of mass)

Number of atoms = N * (density) * volume / (Molecular Weight) where N is Avogadro's Number (6.022x10^23) and the molecular weight is easily found on a periodic table of elements, copper is 63.546.

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