Question

Calculate the density of metal with molar mass 56 g mol^{- 1} that crystallises to form a bcc structure with edge length 288 pm.

Options

• 9.8 g cm^-3

• 5.8 g cm^-3

• 8.7 g cm^-3

• 7.8 g cm^-3

Answer 1

7.8 g cm^-3

Explanation:

For bcc structure,

Number of atoms per unit cell (Z) = 2

Edge length (a) = 288 pm = `2.88 xx 10^-12` cm

Molar mass (m) = 56 g mol^-1

Avagadro's number (N_A) = `6.023 xx 10623`

Now, density `(rho) = ("Z" xx "M")/("a"^3 xx "N"_"A")`

`= (2 xx 56)/((2.88 xx 10^-12)^3 xx 6.023 xx 10^23)`

= 7.78 g cm^-3 ≈ 7.8 g cm^-3