An element crystallizes in a face-centered cubic (fcc) lattice with a unit cell edge length of 200 pm. The density of the element is 2.5 g cm ⁻³ . If a sample of the element has a mass of 2.0 g, the total number of atoms present in the sample is x 10²³ . The value of x is ________.

Step-by-step solution

For an fcc lattice, the effective number of atoms per unit cell, Z = 4 . Edge length, a = 200 pm = 2 10⁻⁸ cm. Volume of one unit cell, V_ cell = a^3 = (2 10⁻⁸)^3 = 8 10⁻²⁴ cm ^3 . Total volume of the given sample, V_ total = Mass Density = 2.0 2.5 = 0.8 cm ^3 . Number of unit cells in the sample = V_ total V_ cell = 0.8 8 10⁻²⁴ = 10²³ . Total number of atoms = Z ( Number of unit cells ) = 4 10²³ . Comparing with x 10²³ , we get x = 4 . Answer: 4