# How do you calculate the relative atomic mass of isotopes?

Jul 10, 2017

This is basically a ratio math problem.

#### Explanation:

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.

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.

If you want to calculate the relative amounts OF different isotopes in a sample, the process is essentially reversed. By reacting a known mass of an element with another known quantity (e.g. forming chlorides) you can compare the before/after masses to find tihe relative amounts of the isotopes.

An element or compound could also be analyzed by a mass spectrometer, which separates the isotopes by mass and indicates the relative amount by the amount of signal generated by each isotope.