Question

a metal element has a density of 7.87 g/cm3 and an atomic mass of 55.85 g/mol. It crystallizes wiht a cubic unit cell, with an edge length of 286.7 pm. Calculate the number of atoms per unit cell.

Answer 1

Answer: 2

Explanation: A. Metal having density of 7.87g/cm3.

Atomic mass of 55.85g/mol.

Edge length 286.7pm.

The formula used is for density as

Density = No. Of atoms per unit cell* mass of atom/edge length ^3* avogadro number

Answer 2

Number of atoms per unit cell are :

• Given: Density of metal element = 7.87 g/cm3

Atomic mass = 55.85 g/mol.

Edge length =286.7pm=286.7 × 10^-10cm

• We know that,

• Density, D = Z× M/a^3×Na

• Where, Z = Number of atoms per unit cell

M = Atomic mass

a = edge length

Na = Avogadro number

• Z = D×a^3×Na / M

=7.87 g/cm3 × (286.7 × 10^-10cm)^3 × 6.023×10^23 / 55.85 g/mol.

• Calculate, you'll get Z = 2