Guide
Reading Isotopes and Atomic Mass
Look at chlorine on the periodic table and you will see 35.45. No chlorine atom has that mass. Look at technetium and you will see 98, a bare whole number with no decimals at all, which is not an average of anything. Neither of these is a misprint - they are two different kinds of number sharing one column of the table, and knowing which is which explains a great deal about how the table was built.
This guide untangles the three quantities that all get loosely called 'atomic mass': the mass number of an isotope, the actual mass of that isotope, and the standard atomic weight printed on the table. Then it shows how to calculate the third from the other two, using chlorine, copper and boron as worked examples you can check against ChemTable's own figures.
What an isotope is
Every atom of an element has the same number of protons - that count is what makes it that element. The number of neutrons, however, can vary, and atoms of one element with different neutron counts are called isotopes. Chlorine always has 17 protons; a chlorine atom with 18 neutrons and one with 20 neutrons are both entirely and unambiguously chlorine.
Because chemistry is driven by electrons, and isotopes of an element share the same electron configuration, isotopes are chemically almost indistinguishable. What they differ in is mass, and so in the things mass governs: rates of diffusion, small shifts in reaction rate, and nuclear stability. That is why isotopes have to be separated by physical means such as centrifugation rather than by any chemical reaction.
Three masses, three meanings
Most confusion here comes from using one phrase for three quantities. Keeping them apart makes the rest straightforward.
The reason isotopic masses are not exactly whole numbers is twofold: a proton and a neutron do not each weigh exactly 1 u, and binding the nucleus together converts a small amount of mass into energy, leaving the assembled nucleus slightly lighter than its parts. Carbon-12 is the sole exception, and only because the unit is defined from it.
- Mass number (A): protons plus neutrons. Always a whole number. Chlorine-35 has A = 35.
- Isotopic mass: the measured mass of one atom of that isotope, in unified atomic mass units (u). Chlorine-35 is 34.9689 u - close to 35, but not equal to it.
- Standard atomic weight: the abundance-weighted average across the isotopes found in ordinary terrestrial material. Chlorine's is 35.45, a value no individual atom has.
- 1 u is defined as exactly one twelfth the mass of a carbon-12 atom, which is why carbon-12 weighs exactly 12 u by definition.
Isotope notation
Written in full, an isotope carries its mass number as a superscript and its atomic number as a subscript in front of the symbol, giving ³⁵Cl and ³⁷Cl, both with Z = 17. Because the symbol already fixes the proton count, the subscript is usually dropped as redundant, and in running text the isotopes are simply spelled out as chlorine-35 and chlorine-37.
The neutron count is whatever is left over: A − Z. Chlorine-35 has 35 − 17 = 18 neutrons and chlorine-37 has 20. This also makes clear what an isotope is not. Changing the neutron count gives a different isotope; changing the electron count gives an ion, Cl⁻ rather than Cl, with the same mass but a different charge. The two ideas are unrelated and are often mixed up.
The weighted average, worked
A standard atomic weight is the sum of each isotope's mass multiplied by its fractional abundance. Chlorine is the classic worked example because it has just two stable isotopes in a memorable ratio.
- Write down each isotope's mass and abundance: chlorine-35 at 34.9689 u and 75.76%, chlorine-37 at 36.9659 u and 24.24%.
- Convert the percentages to decimal fractions: 0.7576 and 0.2424. They must add to 1.
- Multiply each isotopic mass by its fraction: 34.9689 × 0.7576 = 26.4924, and 36.9659 × 0.2424 = 8.9605.
- Add the contributions: 26.4924 + 8.9605 = 35.4529.
- Round to the precision your data supports: 35.45, exactly the value ChemTable lists for chlorine.
More examples from the table
Copper reads 63.546, and the same calculation reproduces it. Copper has two stable isotopes: copper-63 at 62.9296 u with 69.15% abundance, and copper-65 at 64.9278 u with 30.85%. The contributions are 62.9296 × 0.6915 = 43.5158 and 64.9278 × 0.3085 = 20.0302, which add to 63.546. The average sits much closer to 63 than to 65 because the lighter isotope is more than twice as common - a weighted average always leans toward the abundant isotope.
Carbon's 12.011 works the same way and shows how small a minority isotope's effect can be. Carbon-12 is exactly 12 u and makes up about 98.9% of natural carbon, while carbon-13 is 13.00335 u and about 1.1%. The sum 12 × 0.9893 + 13.00335 × 0.0107 comes to 12.011, so the entire 0.011 above the whole number is the contribution of carbon-13.
Boron's 10.81 comes from boron-10 at 10.0129 u and about 19.9%, plus boron-11 at 11.0093 u and about 80.1%, giving 1.9926 + 8.8184 = 10.811. Boron is also one of a small group of elements whose isotopic composition varies measurably between natural sources, so IUPAC now publishes its standard atomic weight as an interval rather than a single figure. Reference tables quote a conventional value from inside that interval so that ordinary calculations have something usable.
When there is no average to take
Some elements have no stable isotopes and no characteristic terrestrial composition, so there is simply nothing to average. Technetium and promethium are the two gaps in the otherwise unbroken run of stable elements below bismuth, and everything from polonium upward is radioactive. For these the convention is to quote the mass number of the longest-lived known isotope instead, which is why ChemTable lists technetium as 98 and promethium as 145, plutonium as 244 and americium as 243 - whole numbers, because a mass number is always a whole number.
The distinction matters when you calculate a molar mass. For an ordinary element you are using an average over a real mixture that any sample will reproduce. For technetium you are using one isotope's mass number by convention, and a different isotope would give a different figure. It is a placeholder that lets the arithmetic proceed, not a measurement of a sample anyone routinely handles.
Elsewhere on the table the averages get their character from the number of isotopes involved. Tin has ten stable isotopes, more than any other element, and its 118.71 is a blend of all of them. Hydrogen sits at the other extreme: natural hydrogen is overwhelmingly protium with a single proton and no neutron, with only a trace of deuterium, which is why its standard atomic weight of 1.008 is barely above one. Open any element in ChemTable and the atomic mass you see is the end result of exactly this kind of weighting.
Frequently asked questions
What is the difference between mass number and atomic mass?
Mass number counts protons plus neutrons in one specific isotope and is always a whole number. The atomic mass on the periodic table is an abundance-weighted average across an element's natural isotopes, so it usually is not.
Why is chlorine 35.45 when no chlorine atom weighs that?
Because it is an average. Natural chlorine is about 75.76% chlorine-35 at 34.9689 u and 24.24% chlorine-37 at 36.9659 u, and 34.9689 × 0.7576 plus 36.9659 × 0.2424 gives 35.45.
Do isotopes of an element react differently?
Barely. They have identical electron configurations and so essentially identical chemistry. Their different masses can shift reaction rates slightly and change nuclear stability, but no chemical test separates them.
Why do some elements show a whole number with no decimals?
Those elements have no stable isotopes and no fixed natural composition, so no average exists. The table shows the mass number of the longest-lived known isotope instead, as with technetium at 98 and promethium at 145.