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How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.

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How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.

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Given,

We know the dimension and density of its unit cell.

Let,

The edge length of a unit cell = a

The volume of the cell = a3

Density = d

Atomic mass = M

Mass of unit cell = No. of atoms in unit cell x Mass of each atom = Z × m

Mass of an atom present in the unit cell, m = M/ Na

where Na is the Avogadro’s number.

We know, d = Mass of unit cell / Volume of unit cell = Zm/a3 = Z.M /a3Na

Therefore, Atomic mass, M =( da3Na) / Z

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