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.

  • 2
    $\begingroup$ I think this should be on Chemistry SE. $\endgroup$ – Argon Jan 26 '13 at 23:56
  • $\begingroup$ Once you get your answer, don't forget that the question in the title is about cubic centimeters, not cubic meters. $\endgroup$ – Gerry Myerson Jan 26 '13 at 23:57
  • 1
    $\begingroup$ @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? $\endgroup$ – Gerry Myerson Jan 26 '13 at 23:58
  • $\begingroup$ @Asaf, done.${}$ $\endgroup$ – 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 $n$.


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.