Question

What is the density of iron crystal which crystallizes in body-centred cubic structure with edge length 287 pm? (At. mass of Fe = 56 amu)

Options

• 7.87 g/cm³

• 6.07 g/cm³

• 7.07 g/cm³

• 6.87 g/cm³

Answer 1

7.87 g/cm³

Explanation:

Density = `("n" xx "M")/("N"_"A" xx "a"^3)`

a = 287 × 10^-12 m = 287 × 10^-10 cm

For BCC, n = 2

`rho = (2 xx 56)/(6.022 xx 10^23 xx (287 xx 10^-10))` cm

`= 112/(1.423 xx 10^8 xx 10^-7)`

`= 112/(1.423 xx 10)`

`= 112/14.23`

= 7.87 g/cm³