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This problem involves mathematical reasoning concerning elements of chemistry. For an introduction to mass spectrometry read our article Inspect Your Gadgets.
A diatomic gas of an element with a single stable isotope is analysed in a mass spectrometer. How many peaks will there be? How many peaks will there be if the element forming a diatomic gas has $2$ or $3$ stable isotopes?
When water is analysed in a mass spectrometer there are peaks at relative atomic mass $17$ and $18$. What chemicals do these peaks correspond to? Why are there no peaks at $1$ and $16$?
A compound is analysed and has peaks at $35, 37, 70, 72$ and $74$. What is this compound?
Another compound has peaks at $12, 13, 14, 15, 16$. What might this be? What is it definitely not?
Another compound has peaks at $14, 15, 16, 17$. What might this be? What is it definitely not?
A mixture of two chemicals is analysed and has peaks at $35, 36, 37, 38$ and $40$. What might this be? What is it definitely not?
Extension: A final compound has peaks at (from tallest to smallest) $31, 45, 29, 27, 46, 43, 26, 30, 15, 42, 28, 19, 25, 14, 13, 41, 47, 44, 17, 24, 18, 33, 12$. Can you suggest a likely candidate for the compound? What could the various peaks correspond to?
Other mathematical chemistry problems can be found on the chemNRICH pages.