How can you calculate the relative abundance of two isotopes when given the atomic masses of both isotopes and also the average atomic mass for the element?
Igloo says The conventional method is to use algebra. Lets take an example. Copper consists mainly of two isotopes, 63Cu and 65Cu, and its (average) atomic mass is 63.55 (to 2 d.p.) Lets assume next that the percentage abundance of 63Cu is x This means that the percentage abundance of 65Cu will be 100-x Given 100 random copper atoms, x will each have a mass of 63 [total mass = 63x] And 100-x will have a mass of 65 [total mass = (100-x) x 65 = 6500-65x] So the total mass of 100 atoms = 63x + 650065x = 65002x This means that the average mass = (65002x) / 100 But we are told in the question that average mass = 63.55 Therefore (6500-2x) / 100 = 63.55 So 65002x = 6355 Hence 2x = 6500-6355 = 145 And x = 72.5 So, in a typical sample of copper 72.5% of the atoms are 63Cu and 27.5% are 65Cu. Another (shorter) method is to use a number scale and intuition, but perhaps you are safer with algebra! Risk assessment Before attempting any practical work based on the advice and suggestions on this webs
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