How Do You Calculate Relative Atomic Mass From Isotope Abundance?

Multiply each isotope's mass by its abundance, add the products, and divide by the total abundance. This gives the weighted mean, because more abundant isotopes contribute more to the element's relative atomic mass.

The Calculation Method

For isotopes with percentage abundances:

$$A_r = \frac{(m_1 \times a_1) + (m_2 \times a_2) + \cdots}{100}$$

Here, $m$ is the isotope's relative isotopic mass, $a$ is its percentage abundance, and $A_r$ is the relative atomic mass. If abundances are written as decimals that add to $1$, do not divide by $100$.

The relative atomic mass, $A_r$, is the weighted mean mass of an atom of an element relative to one-twelfth of the mass of a carbon-12 atom. It has no unit because it is a relative value.

In a mass spectrum, the relative intensity of each isotopic peak represents its relative abundance. The calculation combines those particle-level proportions into one average value for a naturally occurring sample. Always confirm that the abundances total $100\%$, allowing for small rounding differences.

Worked Example

A sample of chlorine contains 75.77% chlorine-35 and 24.23% chlorine-37.

Therefore:

$$A_r = \frac{2651.95 + 896.51}{100} = 35.4846 \approx 35.48$$

The answer lies closer to 35 than 37 because chlorine-35 is more abundant. Using more precise isotopic masses, rather than mass numbers $35$ and $37$, may produce a slightly different answer; follow the data given.

A common misconception is to calculate the ordinary mean, $(35+37)/2=36$. This is incorrect unless both isotopes have equal abundances. Another mistake is dividing by the number of isotopes rather than by $100$.

IB Exam Technique

This is assessed for both SL and HL in Structure 1.2: The nuclear atom. For a calculate question, show the weighted-mean substitution and working, use the isotopic masses supplied in the question, and give a sensible number of significant figures. Check that your answer lies between the smallest and largest isotope masses and is closest to the most abundant isotope.