Question

The density of chromium is 7.2 gm cm 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​

Answer 1

Given:

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.