Question:

A metallic element exists as cubic lattice. Each edge of the unit cell is $2.88 \, \mathring A$. The density of the metal is 7.20 g $cm^{-3}$. How many unit cell will be present in 100 g of the metal?

Updated On: Jul 5, 2022
  • $6.85 \times 10^2$
  • $5.82 \times 10^{23}$
  • $4.37 \times 10^5$
  • $2.12 \times 10^6$
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The Correct Option is B

Solution and Explanation

The volume of the unit cell $= (2.88 \, \mathring A )3 = 23.9 \times 10^{-24} \, cm^3$. The volume of 100 g of the metal $ = \frac{m}{\rho} = \frac{100}{7.20} = 13.9 \, cm^3$ Number of unit cells in this volume $ = \frac{13.9 \, cm^3}{23.9 \times 10^{-24} \, cm^3} = 5.82 \times 10^{23}$
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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.