Isotopes and atomic mass

The periodic table lists chlorine as about 35.45, yet no chlorine atom weighs 35.45. Every one is either chlorine-35 or chlorine-37.

Same element, different weights

Isotopes of an element have the same number of protons and electrons, so they behave the same way in reactions. They differ only in neutrons, which changes their mass. Hydrogen shows this clearly. Ordinary hydrogen has no neutron at all. Deuterium has one and is about twice as heavy. Tritium has two and is radioactive. NIST measures 99.9885% of natural hydrogen as the plain kind and 0.0115% as deuterium.

Where 35.45 comes from

The atomic weight printed on the periodic table is an average over all the atoms of that element found in nature, weighted by how common each isotope is. Masses are measured in atomic mass units, where one carbon-12 atom is exactly 12. For chlorine, NIST gives chlorine-35 a mass of 34.969 and a share of 75.76%, and chlorine-37 a mass of 36.966 and a share of 24.24%.

Multiply each mass by its share and add: 34.969 × 0.7576 + 36.966 × 0.2424 ≈ 26.49 + 8.96 ≈ 35.45. Because three out of four chlorine atoms are the lighter kind, the average sits much closer to 35 than to 37. The same sum for carbon, 12 × 0.9893 + 13.003 × 0.0107, gives about 12.011, which is why carbon is listed a little above 12.

Notice that the isotope masses are close to whole numbers but not exactly equal to them. Chlorine-35 has a mass number of 35, a simple count of 17 protons and 18 neutrons, yet its measured mass is 34.969. Mass numbers are always whole numbers, while measured masses are not, because protons and neutrons are not exactly 1 unit each and some mass is used up in binding the nucleus together.

NIST does not give chlorine a single atomic weight. It gives a range, from 35.446 to 35.457, because the share of chlorine-37 varies slightly between samples from different places. For everyday work chemists round it to 35.45. A few other elements, including hydrogen and carbon, are listed with ranges for the same reason.

Unstable isotopes

Some isotopes are unstable and slowly change into other elements by giving off radiation. Carbon-14 is one of them. NIST notes that half of any amount of carbon-14 turns into nitrogen-14 over 5,730 years. That steady rate is called a half-life. Living things take in carbon, including a tiny share of carbon-14, all their lives. After they die, the carbon-14 is no longer topped up and its share halves every 5,730 years, so measuring what is left tells archaeologists how old a bone, a seed or an old campfire is.

Most isotopes you meet are stable. Carbon-12 and carbon-13 never change on their own, and neither do the two chlorine isotopes or ordinary hydrogen and deuterium. Of the eight isotopes in the table above (D is deuterium and T is tritium; shares are NIST values), only tritium and carbon-14 are radioactive.