Question

What is the atomic mass of lithium if $7.42\%$ of its atoms have the mass of $6.02amu$ and $92.58\%$ of its atoms have the mass of $7.02amu$?

Answer 1

We need to understand the concept of calculating the average of the given substances with respect to its percentage existence. An average is always the sum of the number divided by the number of entities. We shall first explain this concept using simple whole numbers and their percentages and then calculate the average atomic mass of the given entities.

Complete answer:
Let us first calculate the average of numbers $1,2,3\& 4$ to understand the concept of calculating average. The average of $1,2,3,4$ is $\dfrac{{1 + 2 + 3 + 4}}{4} = 2.5$. We now consider the percentages of these numbers. Let there be $25\%$ of number $1$, $30\%$ of number $2$, $35\%$ of number $3$ and $40\%$ of number $4$. The average can be calculated by multiplying the numbers with their respective percentages and then adding them up.
Hence the average is $\left( {0.25 \times 1} \right) + \left( {0.30 \times 2} \right) + (0.35 \times 3) + (0.40 \times 4)$= $2.5$
Similarly, we can calculate the atomic mass of lithium if $7.42\%$ of its atoms have the mass of $6.02amu$ and $92.58\%$ of its atoms have the mass of $7.02amu$. Hence the average atomic mass will be:
$(0.724 \times 6.02) + (0.9258 \times 7.02)$= $6.9458amu$
Rounding this calculated value up to two decimal places, we get $6.9458amu$.
Therefore, the atomic mass of lithium if $7.42\%$ of its atoms have the mass of $6.02amu$ and $92.58\%$ of its atoms have the mass of $7.02amu$. Hence the average atomic mass is $6.9458amu$.

Note:
We must be noted that Lithium is made up of two stable isotopes, lithium-$6$ and lithium-$7$, the latter of which is much more abundant, accounting for $92.5$ percent of the atoms in nature. The more abundant an isotope is, the more its influence on the average atomic mass. The percentages given are also known as abundance which is divided by $100$ in using it to calculate the average atomic mass.