1. Tardigrade
  2. Question
  3. Chemistry
  4. X-ray diffraction studies show that Cu crystallises in face centred cubic unit cell with cell edge of 3.608 × 10-8 cm. An another experiment shows that Cu is determined to have a density of 8.92 g / cm 3. Find out the atomic mass of copper.

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Q. $X$-ray diffraction studies show that $Cu$ crystallises in face centred cubic unit cell with cell edge of $3.608 \times 10^{-8} cm$. An another experiment shows that $Cu$ is determined to have a density of $8.92\, g / cm ^{3}$. Find out the atomic mass of copper.

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Solution:

In case of $fcc$ lattice, number of atoms per unit cell, $Z=4$.
We know that, $M=\frac{d N_{A} a^{3}}{Z}$
$\therefore M=\frac{8.92\, g / cm ^{3} \times 6.022 \times 10^{23} atom\, mol ^{-1}\times\left(3.608 \times 10^{-8} cm \right)^{3}}{4 \text { atom }}=63.1\, g / mol$