Question

X- ray diffraction studies shows that copper crystallises in an fcc unit cell with edge
length of 3.608 × 10-8 cm. In a separate experiment copper is determined to have a
density of 8.92 g/cm3 , calculate the atomic mass of copper.
( answer is 63.1 g/mol)

Answer 1

Given:

Edge length = 3.608 × 10⁻⁸ cm

Density = 8.92 gcm⁻³

To find:

Atomic mass of copper

Solution:

According to X- ray diffraction, the copper crystallizes in an fcc unit cell.

means,    Z = 4

here, Z = no. of atoms per unit cell

Formula used to determine the given mass is-

       $D = \frac{Z \times M}{a^3}$

here, D = density of crystal lattice

        Z = no. of atoms per unit cell

        M = given mass

         a = edge length

or,       $M = \frac{D \times a^3}{Z}$

so, by substituting all the values we get,

          $M = \frac{8.92 \times (3.608 \times 10^-^8)^3}{4}$

          $M = \frac{8.92 \times 46.97 \times 10^-^2^4}{4}$

         M = 104.74 × 10⁻²⁴g

Now, to find atomic mass we have,

  atomic mass = given mass × Nₐ

here, Nₐ = Avogadro's  number = 6.023 × 10²³

 atomic mass = 104.74 × 10⁻²⁴g × 6.023 × 10²³ mol⁻¹

 atomic mass =  630 × 10⁻¹

atomic mass = 63 gmol⁻¹

Therefore, atomic mass is found to be 63 gmol⁻¹.