Question

How do you calculate the atomic mass of element $X$ if there are two isotopes of this element ( $X - 24$ and $X - 28$ ) and $75\%$ of all $X$ atoms are $X - 28$ isotopes?

Answer 1

We need to understand the concept of calculating the atomic of the given isotopes with respect to its percentage existence. We shall first explain this concept using simple whole numbers and their percentages and then learn how to calculate the atomic mass of the given entities. The more abundant an isotope is, the more its influence on the atomic mass of the element.

Complete step by step answer:
Let us first calculate the mass of an element having four isotopes of masses 1, 2, 3 and 4 whose percentage existence are given. This can be calculated by calculating the average since there are more than one entity. Let $25\%$ of number $1$, $30\%$ of number $2$, $35\%$ of number $3$ and $40\%$ of number $4$ be the percentage existence. The average can be calculated by multiplying the numbers with their respective percentages and then adding them up. Hence the average is $\left( {0.25 \times 1} \right) + \left( {0.30 \times 2} \right) + (0.35 \times 3) + (0.40 \times 4) = 2.5$
Now for the given element $X$, two isotopes are $X - 24$ and $X - 28$ and $75\%$ of all $X$ atoms are $X - 28$ isotopes. Hence it is obvious that the remaining $25\%$ of the $X$ atoms are of the $X - 24$ isotope since there are only two isotopes.
If the masses of the given isotopes are given, we can calculate the average atomic mass of the element by multiplying the numbers with their respective percentages and then adding them up. The formula can be given as $\sum (mass \times percentage)$.

Note: It must be noted that the percentages given are also known as abundance which is divided by $100$ for using it in the formula to calculate the average atomic mass. Since the given element has two isotopes whose percentage abundances are different hence the average is to be calculated. For example, the average atomic mass of rubidium if $71.17\%$ of its atoms have a mass of $84.92amu$ and $27.3\%$ of its atoms have a mass of $86.91amu$ is $85.47$ $amu$.