An unknown metal with an atomic mass of 60 u crystallizes in a cubic unit cell. The approximate density of the crystal is given by the expression 200 x^3 g cm ⁻³ , where x is the edge length of the unit cell in . Which of the following represents the type of cubic lattice the metal crystallizes in? [Take Avogadro's number N_A 6.0 10²³ mol ⁻¹ ]

Step-by-step solution

The formula for the density of a cubic unit cell is: = Z M N_A a^3 where Z is the number of atoms per unit cell, M is the atomic mass, N_A is Avogadro's number, and a is the edge length in cm. Given edge length a = x = x 10⁻⁸ cm . Therefore, a^3 = x^3 10⁻²⁴ cm ^3 . Substituting the given values into the density formula: = Z 60 6.0 10²³ (x^3 10⁻²⁴) = Z 60 6.0 10⁻¹ x^3 = Z 60 0.6 x^3 = 100 Z x^3 g cm ⁻³ We are given that the density is approximately 200 x^3 g cm ⁻³ . Equating the two expressions: 100 Z x^3 = 200 x^3