How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its uni

Exercises · 1.5

Q. 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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Step 1 – Mass of one unit cell (two ways).

m_{\text{cell}} = d\times V = d\,a^3 \qquad\text{and}\qquad m_{\text{cell}} = z\times\frac{M}{N_A}

where $z$ = number of atoms per unit cell and $M/N_A$ = mass of one atom.

Step 2 – Equate.

d\,a^3 = \frac{zM}{N_A}

Step 3 – Solve for the atomic mass.

$\boxed{M = \frac{d\,a^3 N_A}{z}}$ …

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