Question

A substance crystallizes in cubic, zinc blende
structure. Its density is 1000 kg m-3. When it
was compressed, the cell parameter decreased
from 100.1 pm to 100 pm. Calculate the density
of the substance in the compressed state.
(Give the answer in units of kg m-3, nearest to
the whole number)​

Answer 1

Given info : A substance crystallizes in cubic, zinc blende structure (fcc). Its density when it was compressed is 1000 kg/m³ . The cell parameter decreased 100.1 pm to 100 pm.

To find : the density of substance in the compressed state.

solution : We know, density , d = ZM/Na³

Where Z is no of atoms per unit cell, M is molar mass, N is Avogadro's number and a is edge length of cubic unit cell.

here Z , M and N are constant

So, d ∝ 1/a³

i.e., d₁/d₂ = (a₂/a₁)³

Here, d₁ = 1000 kg/m³, d₂ = ?, a₁ = 100.1 pm and a₂ = 100 pm

Now, (1000/d₂) = (100/100.1)³

⇒1000/d₂ = (1/1.001)³

⇒d₂ = 1000 × (1.001)³

= 1000 [1 + 1/1000]³

From binomial expansion, (1 + x)ⁿ ≈ 1 + nx where 1 >> x

so, (1 + 1/1000)³ ≈ 1 + 3/1000 = 1.003

so, d₂ = 1000 × 1.003 = 1003 kg/m³

Therefore density of substance in the compressed state is 1003 kg/m³

Answer 2

Answer:1003

Explanation: