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# How is the atomic mass of an element calculated from isotope data?

Apr 14, 2016

This is basically a ratio math problem. We combine known percentages of have several different masses into a weighted-average mass by multiplying each mass by the weight percent and adding them up.

#### Explanation:

For example, Thallium consists of 29.5% Tl-203 and 70.5% Tl-205. What is the relative atomic mass of thallium? We have two different masses and a known percentage of each.

0.295 x 203 + 0.705 x 205 = 59.885 + 144.525 = 204.4
This is what we would expect – a slight “shift” to the higher mass from the 50/50 average of 204 because of the larger percentage of Tl 205 in the sample.

NOTE that this doesn't mean that any atom of an element is actually this value! Individual atoms will have the specific masses as indicated by our isotope analysis.

The “average” value is used as a general calculation approximation for the element. Specific research objectives often require precise knowledge of the actual mass value of an element under study.