Question:

An element crystallises in a structure having a $fcc$ unit cell of an edge $200\,pm$. If $200\,g$ of this element contains $24 \times 10^{23}$ atoms then its density is

Updated On: Jul 6, 2022
  • $41.66\,g\,cm^{-3}$
  • $313.9\,g\,cm^{-3}$
  • $8.117\,g\,cm^{-3}$
  • $400\,g\,cm^{-3}$
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The Correct Option is A

Solution and Explanation

Molar mass of the element $=\frac{200}{24\times10^{23}}\times6.023\times10^{23}$ $=50.19\,g\,mol^{-1}$ For $fcc, Z=4$, $V=a^{3}=\left(200\times10^{-10}\right)^{3}$ $d=\frac{Z\times M}{N_{A}\,\times V}$ $=\frac{4\times50.19}{6.023\times10^{23}\times\left(200\times10^{-10}\right)^{3}}$ $=41.66\,g\,cm^{-3}$
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Notes on The solid state

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.