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Chapter 1: Q59. (page 20)

One mole of atoms consists of individual atoms. If a mole of atoms were spread uniformly over the Earth鈥檚 surface, how many atoms would there be per square meter?

Short Answer

Expert verified

There would be 1.2脳109atoms/m2over the surface of the Earth.

Step by step solution

01

Step 1. Identification of the given data

An atom is the smallest unit in any matter, whether solid, liquid, gas, or plasma.

In one mole, there are 6.02脳1023atoms.

Let the radius of the Earth be R=6.4脳106m.

02

Step 2. Determination of the surface area of the Earth

The surface area of the Earth is:

A=4蟺R2=4脳227脳6.4脳106m2=5.1脳1014m2

03

Step 3. Determination of the number of atoms per unit area

The expression for the number of atoms per unit area is:

N=Totalnumberofatomsin1moleTotalsurfacearea

Substituting the numerical values in the above expression,

N=6.02脳1023atoms5.1脳1014m2=1.18脳109atoms/m2鈮�1.2脳109atoms/m2

Thus, there are 1.2脳109atoms/m2of the Earth鈥檚 surface area.

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