Question

Predict the type of cubic lattice of a solid element having edge length of 400 pm and density is 6.25 g/ml.
(Atomic mass of element = 60)

Answer 1

Given:

Edge length a = 400 pm = 400 × 10⁻¹² m = 400 × 10⁻¹² cm = 4 × 10⁻⁸ cm

a³ = (4 × 10⁻⁸ cm)³ 

= 64 × 10⁻²⁴ cm³ 

ρ = 6.25 g/mL = 6.25 g.cm⁻³

M = 60 

To find:

n = ?

Formula:

ρ = `("M"xx"n")/("a"^3xx"N"_"A")`

6.25 = `(60xx"n")/(64xx10^-24xx6.022xx10^23)`

6.25 = `(60xx"n")/(6.4xx6.022)`

n = `(6.25xx6.4xx6.022)/60`

n = `(6.25xx6.4)/10`

n = 4 

Hence, the type of cubic lattice is FCC, as 4 particles are present per unit cell.