Question:

At $T( K )$, copper (atomic mass $=63.5\, u$ ) has fcc unit cell structure with edge length of $x \mathring {A}$. What is the approximate density of $Cu$ in $g \,cm ^{-3}$ at that temperature? $\left(N_{A}=6.0 \times 10^{23} mol ^{-1}\right)$

Updated On: Apr 4, 2024
  • $\frac{42.3}{x^3}$
  • $\frac{4.23}{x^3}$
  • $\frac{423}{x^3}$
  • $\frac{212}{x^3}$
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The Correct Option is C

Solution and Explanation

Given,

fcc unit cell is present, $Z=4$

Edge length $=x\, ?$

Atomic weight $=63.5 \,g \,mol ^{-1}$
$\because$ Density, $d=\frac{Z \times \text { atomic weight }}{a^{3} \times N_{A}}$

where, $a=$ edge length

$d =\frac{Z \times \text { atomic weight }}{x^{3} \times 6.023 \times 10^{23} \times\left(10^{-8}\right)^{3}} $
$=\frac{4 \times 63.5}{x^{3} \times 6.023 \times 10^{23} \times 10^{-24}}$
$d =\frac{423.0}{x^{3}}$
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Concepts Used:

Solid State

Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions. 

Solid State

Types of Solids:

Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;

  • Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
  • Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.