Question

A compound has fcc structure. If density of unit cell is 3.4 g cm⁻³, what is the edge length of unit cell?

(Molar mass = 98.99)

Options

• 8.780 Å

• 6.083 Å

• 5.783 Å

• 7.783 Å

Answer 1

5.783 Å

Explanation:

Given, Density (d) = 3.4 g cm⁻³

Molar mass (M) = 98.99 g/mol

N_A = 6.023 × 10²³

For fcc emit cell, Z = 4

We know that, edge length (a³) = `("M" xx "Z")/("d" xx "N"_"A")`

= `(98.99  ("g"//"mol") xx 4)/((3.4  "g cm"^-3) xx (6.023 xx 10^23)  "mol"^-1)`

= 193.3 × 10⁻²⁴ cm⁻³

= 5.783 × 10⁻⁸ cm ......[1 Å = 1 × 10⁻⁸ cm]

= 5.783 Å