Chemistry Clarity · chemistryclarity.com

Isotopes and Average Atomic Mass

How do you calculate average atomic mass from isotopes?

IntermediateAtomic Structure & PeriodicityLast reviewed 3 October 2026
Download lesson (PDF)

What is it?

Most elements exist naturally as a mixture of isotopes: atoms with the same number of protons but different numbers of neutrons, and therefore different masses.

The atomic mass printed on the periodic table is the weighted average mass of an element’s atoms, taking into account how common each isotope is (its natural abundance).

Key idea

The periodic-table atomic mass is an average weighted by abundance. That’s why chlorine is 35.45 u and not a whole number: no single chlorine atom has a mass of 35.45 u.

Why does it matter?

  • Every calculation with molar mass uses it. When you calculate moles from grams, you rely on average atomic masses, because real samples contain the natural mix of isotopes.
  • Isotopes are useful in their own right. Carbon-14 is used to date ancient materials, and other isotopes are used in medical imaging and as tracers to follow chemical reactions.
  • It explains the periodic table. Seeing that atomic masses are averages removes the mystery of the decimals.

How does it work?

1. Measuring isotopes

A mass spectrometer separates atoms (as ions) by mass. It measures the mass of each isotope and its relative abundance: what fraction of all the atoms it makes up.

2. Calculating the weighted average

Multiply each isotope’s mass by its abundance written as a decimal fraction (75.76% → 0.7576), then add the results:

average=∑(fraction×mass)\text{average} = \sum (\text{fraction} \times \text{mass})

where the sum (∑\sum) runs over every isotope of the element.

The abundances of all the isotopes must add up to 100% (a total fraction of 1).

3. The average leans toward the most common isotope

Because chlorine-35 is about three times as common as chlorine-37, the average (35.45 u) is much closer to 35 than to 37.

Think of it like this

Your final course grade might be an exam worth 75% and coursework worth 25%. If you score 35 on the exam and 37 on the coursework, your overall mark isn’t the simple average (36). It’s pulled toward the exam score because the exam counts more. Isotope abundances work the same way: they’re the “weights”.

More precisely

Chlorine exists naturally as ClX2\ce{Cl2} molecules, so a real mass spectrum of chlorine gas also shows molecular peaks (around 70, 72 and 74 u). The diagram below is simplified to show single atoms. Isotope abundances also vary very slightly between natural sources, which is why IUPAC gives some standard atomic weights as a small range. Values such as Cl = 35.45 are conventional rounded values for everyday use.

Visualise it

Simplified mass spectrum of chlorine. Two bars: chlorine-35, mass 34.969 u, abundance 75.76 percent; chlorine-37, mass 36.966 u, abundance 24.24 percent. The weighted average is 35.45 u, the value on the periodic table, closer to 35 than to 37.
Chlorine-35 is about three times as common as chlorine-37, so the average sits near 35.

Worked example

Worked example: Average atomic mass of chlorine

Question: Chlorine-35 (34.969 u) makes up 75.76% of chlorine atoms, and chlorine-37 (36.966 u) makes up 24.24%. Calculate the average atomic mass.

  1. Convert to fractions: 0.7576 and 0.2424 (they add up to 1).
  2. Multiply and add: (0.7576×34.969)+(0.2424×36.966)(0.7576 \times 34.969) + (0.2424 \times 36.966)
  3. =26.493+8.961=35.45= 26.493 + 8.961 = 35.45 u

Answer: 35.45 u, the value on the periodic table.

Worked example: An element with three isotopes

Question: Magnesium consists of magnesium-24 (23.985 u, 78.99%), magnesium-25 (24.986 u, 10.00%) and magnesium-26 (25.983 u, 11.01%). Calculate its average atomic mass.

(0.7899×23.985)+(0.1000×24.986)+(0.1101×25.983)=24.31(0.7899 \times 23.985) + (0.1000 \times 24.986) + (0.1101 \times 25.983) = 24.31 u

Worked example: Finding an abundance from the average

Question: Gallium has two isotopes, gallium-69 (68.926 u) and gallium-71 (70.925 u). Its average atomic mass is 69.723 u. What percentage of gallium atoms are gallium-69?

  1. Let xx = fraction of gallium-69, so gallium-71 is 1−x1 - x.
  2. 68.926x+70.925(1−x)=69.72368.926x + 70.925(1 - x) = 69.723
  3. 70.925−1.999x=69.72370.925 - 1.999x = 69.723, so x=1.2021.999=0.601x = \dfrac{1.202}{1.999} = 0.601

Answer: about 60.1% of gallium atoms are gallium-69 (and 39.9% are gallium-71).

Common mistake

Common mistake: Taking a simple average

Averaging 34.969 and 36.966 gives 35.97 u, which is wrong. The isotopes are not equally common, so each mass must be weighted by its abundance.

Common mistake: Using percentages instead of fractions

Multiplying by 75.76 instead of 0.7576 gives an answer 100 times too big. Convert percentages to decimals first (or divide your final sum by 100).

Common mistake: Confusing mass number with isotope mass

The mass number (35) is a whole-number count of protons and neutrons. The isotope mass (34.969 u) is the measured mass, which is slightly different. Use the isotope masses for accurate averages.

Notation note

  • Periodic-table values are also called relative atomic mass (ArA_\text{r}, no units) or atomic weight, especially in UK courses and in IUPAC terminology.
  • Abundance may be given as a percentage or as a fraction; check which before calculating.

Remember this

Remember this

  • Atomic mass on the periodic table = weighted average of the isotope masses.
  • Average = Σ (fraction × isotope mass), with fractions adding up to 1.
  • The average is closest to the most abundant isotope.
  • Never use a simple average unless the isotopes are equally common.

Test yourself

Check your understanding before moving on.

Flashcards

9 cards

  1. Question
    What does the atomic mass on the periodic table represent?
    Answer

    The weighted average mass of an element's atoms, based on the natural abundance of each isotope.

  2. Question
    What is natural abundance?
    Answer

    The percentage (or fraction) of an element's atoms that are a particular isotope.

  3. Question
    How do you calculate an average atomic mass?
    Answer

    Multiply each isotope's mass by its abundance as a decimal fraction, then add the results.

  4. Question
    Why is chlorine's atomic mass (35.45 u) closer to 35 than to 37?
    Answer

    Chlorine-35 is about three times as common as chlorine-37, so it carries more weight in the average.

  5. Question
    What instrument measures isotope masses and abundances?
    Answer

    A mass spectrometer.

  6. Question
    What should the abundances of all an element's isotopes add up to?
    Answer

    100% (a total fraction of 1).

  7. Question
    Boron is 19.9% boron-10 (10.013 u) and 80.1% boron-11 (11.009 u). What is its average atomic mass?
    Answer

    (0.199×10.013)+(0.801×11.009)=10.81(0.199 \times 10.013) + (0.801 \times 11.009) = 10.81 u

  8. Question
    What is the difference between mass number and isotope mass?
    Answer

    Mass number is a whole-number count of protons + neutrons (e.g. 35); isotope mass is the measured mass (e.g. 34.969 u).

  9. Question
    Why is a simple average of isotope masses usually wrong?
    Answer

    Isotopes are not equally common; each mass must be weighted by its abundance.

Quiz

7 questions

  1. Question 1EasyWhy are most atomic masses on the periodic table not whole numbers?
    Show answer

    Answer: They are weighted averages of the masses of an element's isotopes

    Most elements are mixtures of isotopes. The atomic mass is the average of their masses, weighted by how common each isotope is.

  2. Question 2MediumCopper is 69.15% copper-63 (62.930 u) and 30.85% copper-65 (64.928 u). What is its average atomic mass?
    Show answer

    Answer: 63.55 u

    (0.6915 × 62.930) + (0.3085 × 64.928) = 43.516 + 20.030 = 63.55 u. The answer 63.93 u is the simple (unweighted) average.

  3. Question 3EasyAn element has two isotopes with masses 10.0 u and 11.0 u. Its average atomic mass is 10.8 u. Which isotope is more abundant?
    Show answer

    Answer: The 11.0 u isotope

    The average (10.8 u) is closer to 11.0 than to 10.0, so the heavier isotope must be more common.

  4. Question 4MediumBromine is 50.69% bromine-79 (78.918 u) and 49.31% bromine-81 (80.916 u). What is its average atomic mass?
    Show answer

    Answer: 79.90 u

    (0.5069 × 78.918) + (0.4931 × 80.916) = 79.90 u. Using percentages without dividing by 100 gives 7990, 100 times too big.

  5. Question 5MediumLithium is 7.59% lithium-6 (6.015 u) and 92.41% lithium-7 (7.016 u). What is its average atomic mass?
    Show answer

    Answer: 6.94 u

    (0.0759 × 6.015) + (0.9241 × 7.016) = 6.94 u, close to 7 because lithium-7 is far more common.

  6. Question 6HardGallium has two isotopes: gallium-69 (68.926 u) and gallium-71 (70.925 u). Its average atomic mass is 69.723 u. What is the abundance of gallium-69?
    Show answer

    Answer: 60.1%

    Let x = fraction of gallium-69: 68.926x + 70.925(1 − x) = 69.723, so x = 1.202 ÷ 1.999 = 0.601, or 60.1%. 39.9% is the abundance of gallium-71.

  7. Question 7EasyWhich statement about chlorine-35 and chlorine-37 is true?
    Show answer

    Answer: They have different numbers of neutrons

    Both have 17 protons and, as neutral atoms, 17 electrons, so they behave the same chemically. Chlorine-35 has 18 neutrons and chlorine-37 has 20.

Notes and downloads

References

  1. Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Murphy, C. J.; Woodward, P. M.; Stoltzfus, M. W. Chemistry: The Central Science, 15th ed.; Pearson, 2022.

Practise this topic with flashcards and a quiz at chemistryclarity.com/chemistry/isotopes-and-atomic-mass/

Spotted a mistake? Let us know and we'll fix it.