Question

An element has atomic mass 93g mol^-1 and density 11.5 g cm^-3. If the edge length of its unit cells is 300pm, identify the tyoe of unit cell

Answer 1

Hey !!

Question = An element has atomic mass 93 g mol⁻¹ and density 11.5 g cm⁻³ if the edge length of this unit cell is 300pm identify the type of the unit cell ?

Answer = Number of atoms per unit cell, z = d × a³ × NA / M --> (1)

Here, d = 11.5 g cm⁻³ , M = 93 g mol⁻¹ , NA = 6.022 × 10²³ mol⁻¹

                     a = 300 pm = 300 × 10⁻¹⁰ cm = 3 × 10⁻⁸ cm

Now, Substituting these values in the expression (1), we get

     z = 11.5 g cm⁻³ × (3 × 10⁻⁸ cm)³ × 6.022 × 10²³ mol⁻¹ / 93 g mol⁻¹

FINAL RESULT = 2.01

As there are 2 atoms of the element present unit cell, therefore, the cubic unit cell must be body centered.

Hope it helps you !!