A common GCSE question is to calculate the relative atomic mass of an element, given the mass and abundance of a series of isotopes.
e.g., Terrestrial (i.e., as found on Earth) Mg is:
| Mass | 24 | 25 | 26 |
| Abundance | 80% | 10% | 10% |
The Ar is calculated by [(24 x 80%) + (25 x 10%) + (26 x 10%)] / 100% = 24.3
This style of question is also found at A Level. However, a more challenging variation is the reverse calculation: determining the abundance of isotopes given an Ar.
| Question: Magnesium from elsewhere in the universe might have a different set of isotopic abundances. If the abundance of 24Mg is 60% and the Ar = 24.8, determine the abundance of 25Mg and 26Mg. Answer We start by filling in the table as before. The trick is to remember that the abundances of 25Mg and 26Mg must add to up to 40%, so if the abundance of 25Mg = x, then the abundance of 26Mg = 40 – x.
The next step is to write out the equation for Ar then re-arrange to make x the subject [(24 x 60%) + (25x) + (26)(40 – x)] / 100% = 24.8 [(24 x 60%) + (25x) + (26)(40 – x)] = 2480 1440 + 25x + 1040 – 26x = 2480 2480 – x = 2480 –> x = 0 This calculation shows that there must be no 25Mg in this sample so the remainder must be entirely 26Mg i.e., 40% 26Mg. We can now substitute this values of x into the table:
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