You are given a small bar of an unknown metal, M. M\' density is 10.5 g/cm qubed

Question

You are given a small bar of an unknown metal, M. M' density is 10.5 g/cm qubed . the edge of the unit cell is 409pm assuming that metal crystallizes in a face-centered cubic (fcc) lattice, what is M most likely to be? an fcc has 4 atoms. You are given a small bar of an unknown metal, M. M' density is 10.5 g/cm qubed . the edge of the unit cell is 409pm assuming that metal crystallizes in a face-centered cubic (fcc) lattice, what is M most likely to be? an fcc has 4 atoms. assuming that metal crystallizes in a face-centered cubic (fcc) lattice, what is M most likely to be? an fcc has 4 atoms.

Explanation / Answer

Since it is an fcc lattice, therfore there are 4 atoms per unit cell

Let the molar mass of the atom be x g/mole

Thus, density = mass/volume = 4*x/{(6.022*1023)*(409*10-11)3}

or, 10.5 = 4*x/{(6.022*1023)*(409*10-10)3}

or, x = 108.15 g/mole

Thus, the metal 'M' is likely to be Ag i.e silver

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