Question

An element has three isotopes and their isotopic weight are 11, 12, 13 unit their percentage of occurrence in nature is 85, 10, 5 respectively, then calculate the average atomic weight of the element.

Answer 1

Hint: Using the natural abundances of each isotope and on multiplying it with the respective isotopic weight, gives average atomic mass on dividing by 100 and by taking their summation. This is valid for elements with multiple isotopes.

Complete step-by-step answer:
Some atoms have only one isotope, so all their atoms have identical weights but some have two or more isotopes, so their atoms have different masses. All elements obey the law of definite proportions which states that every chemical compound contains fixed and constant proportions (by mass) of its constituent elements.
The term average atomic weight basically denotes relative atomic weight. That’s why they are unitless. Its calculation involves naturally occurring isotopes. Isotopes have the same number of protons but different numbers of neutrons. Since we know, atomic weight is the sum of the number of protons and neutrons, isotopes have different isotopic weights.
Thus, to calculate their average atomic weight, their percentage of occurrence or abundance in nature comes into point. Using these two entities, we can determine the average atomic weight. Here, the formula given below is for the same.
\[average{\text{ }}atomic{\text{ }}weight = \dfrac{{\Sigma (\% abundance \times Atomic{\text{ }}weight)}}{{100}}\]
Putting the given values in it, we get
\[average{\text{ }}atomic{\text{ }}weight = \dfrac{{85 \times 11 + 10 \times 12 + 5 \times 13}}{{100}} = 11.2\]

Hence, the average atomic weight of the element is \[11.2\].

Note: The average atomic weight of an element is found on the periodic table, under the elemental symbol. Whenever we do mass calculations involving compounds or elements, we always tend to use average atomic masses.