Question

barium has bcc structure with radius 288 pm . calculate the density of barium​

Answer 1

Given info : barium has bcc ( body centered cubic) structure with radius 288 pm.

To find : the density of barium

Solution : first find edge length of cubic lattice.

diagonal of cube = 4 × radius of barium

⇒√3l = 4 × 288 pm

⇒l = 665.1 pm

Volume of cube = l³ = (665.1 × 10¯¹²)³

= (6.651 × 10¯¹⁰)³

= 294.2 × 10¯³⁰ m³

number of atoms per unit cell, Z = 1/8 × no of atoms in corners + number of atoms in center of cube

= 1/8 × 8 + 1 = 2

Now density of barium, d = ZM/NV

Where M is atomic mass of barium = 137.33g , N is Avogadro's number = 6.022 × 10²³

now, d = (2 × 137.33 × 10¯³)/(6.022 × 10²³ × 294 × 10¯³⁰) kg/m³

= 1551.34 kg/m³

Therefore the density of barium is 1551.34 kg/m³