An element in its solid phase forms a cubic crystal lattice with mass density 79

Question

An element in its solid phase forms a cubic crystal lattice with mass density 7950 kg/m3 . To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. The smallest spacing between two adjacent atoms is 0.227 nm. What is the element's atomic mass number?

Explanation / Answer

7950 kg/m^3 >> 7950*10^3 g/m^3 Find volume per atom v=a0^3=(.227 * 10^-9 m)^3 Divide 1 m^3 by the volume to find # atoms per m^3 1/V Divide this by avogados number to find moles of atoms 1/(v*A) Divide the # of grams by all of this to get the atomic mass 7950*10^3 g/m^3 / (1/((.227*10^-9)^3*6.02*10^23)) =55.981 g per mole Adjust sigs as needed. This is just about iron

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