Question

Question:Earth has a mass of$5.98\times {10}^{24}kg$ . The average mass of the atoms that make up Earth is 40 u. How many atoms are there in Earth?

Short answer

Answer

The number of atoms in Earth is $9.00\times {10}^{49}$.

Step-by-step solution

Given data

Mass of the earth is$5.98\times {10}^{24}kg$.

The average mass of the atom that makes up Earth is 40 u .

Understanding the conversion factors

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors. Use the mass of earth and mass of atoms to find the number of atoms in Earth.

The expression for the number of atoms is given as follows:

$N=\frac{M\left(Kg\right)}{averagemassofatomsinkg}$ … (i)

Determination of the number of atoms in the earth

The relation between the average mass of atom and kilogram is,

$$\begin{gathered} \text{Soconvert40uintokgas:} \\ \text{M=40u}\left(\frac{1.66\times {10}^{-27}kg}{1u}\right) \\ =6.64\times {10}^{-26}kg \\ \text{Usingequation(i),calculatethenumberofatoms(N)asfollows:} \\ N=\frac{M\left(Kg\right)}{Averagemassofatomsinkg} \\ =\frac{5.98\times {10}^{24}kg}{6.64\times {10}^{-26}kg} \\ =9.006\times {10}^{49}kg \\ \text{Thus,thenumberofatomsinearthis}9.006\times {10}^{49}kg\text{.} \end{gathered}$$