Q21P - Fundamentals Of Physics

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?

Step-by-Step Solution

Answer

Answer

 

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

Step 1: 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  .

Step 2: 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: 

 

    $N=\frac{M\left(Kg\right)}{average mass of atoms in kg}$                                           … (i)

Step 3: Determination of the number of atoms in the earth

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

$$\begin{gathered} \text{So convert 40 u into kg as: } \\ \text{M=40 u}\left(\frac{1.66\times {10}^{-27}kg}{1u}\right) \\ = 6.64\times {10}^{-26}kg \\ \text{ Using equation (i), calculate the number of atoms (N) as follows: } \\ N= \frac{M\left(Kg\right)}{Average mass of atoms in kg} \\ =\frac{5.98\times {10}^{24}kg}{6.64\times {10}^{-26}kg} \\ = 9.006\times {10}^{49}kg \\ \text{ Thus, the number of atoms in earth is }9.006\times {10}^{49}kg\text{. } \end{gathered}$$