Answer
There are $1.76\times 10^{23}$ carbon atoms per $cm^3$
Work Step by Step
A carbon atom consists of 6 protons and 6 neutrons.
The mass of one atom of carbon is $12~u$
We can find the mass of one carbon atom:
$m = (12~u)(1.66\times 10^{-27}~kg/u) = 1.99\times 10^{-26}~kg$
We can find the mass of carbon per $cm^3$:
$m_c = 3500~kg/m^3\times \frac{1~m^3}{10^6~cm^3} = 3.5\times 10^{-3}~kg/cm^3$
We can find the number of carbon atoms per $cm^3$:
$\frac{3.5\times 10^{-3}~kg/cm^3}{1.99\times 10^{-26}~kg/atom} = 1.76\times 10^{23}~atoms/cm^3$
There are $1.76\times 10^{23}$ carbon atoms per $cm^3$.
