The density of chromium is 7.2 gm cm^-3 and crystallises in a body centred cubic lattice with edge length 290pm. The number of atoms present in 30.0 gm of the sample is

Density of chromium, d = 7.2 gm/cm³

Edge length, a = 290 pm = 290 × 10⁻¹⁰ cm

Mass of chromium, w = 30 gm

To Find:

The number of  atoms present in 30 gm of chromium.

Calculation:

Volume of one unit cell, V = a³

 V = (290 × 10⁻¹⁰)³ = 24.39 × 10⁻²⁴ cm³

Volume of 30 gm Chromium = mass × density

V' = 30 × 7.2 = 216 cm³

Total no of unit cells = Total volume / volume of 1 unit cell

N = 216 / 24.39 × 10⁻²⁴

N = 8.856 × 10²⁴

 It is given that chromium crystallises in BCC lattice

No of atoms per unit cell, z = 2

So, total no of atoms =  No of atoms per unit cell × Total no of unit cells

Total no of atoms = 2 × 8.856 × 10²⁴ = 17.712 × 10²⁴

Total no of atoms = 1.77 × 10²⁵

The number of  atoms present in 30.0 gm of the sample is​ 1.77 × 10²⁵.