Atomic mass, moles, and isotopes

A single hydrogen atom has a mass of about 1.67 × 10⁻²⁴ g. The small raised number is an exponent, and a negative one means “divide by 10 that many times,” so written out, this is a decimal point followed by 23 zeros and then 167. Numbers that small are clumsy, so scientists compare atoms on a relative scale and count them in huge batches.

Atomic mass and the dalton

An atom’s mass comes almost entirely from its protons and neutrons. Those two particles have nearly equal masses, and electrons have so little mass by comparison that they’re left out when figuring an atom’s mass.

To compare atoms, scientists take the most common form of carbon, with 6 protons and 6 neutrons, and assign it a mass of exactly 12. An atom’s mass on this relative scale is its atomic mass. A hydrogen atom, with 1/12 the mass of that carbon atom, has an atomic mass of 1. A magnesium atom, with twice the carbon atom’s mass, has an atomic mass of 24.

Atomic mass is measured in daltons (Da), also called atomic mass units (amu). One dalton is 1/12 the mass of the common carbon atom, which is about the mass of one proton or one hydrogen atom. So that carbon atom has a mass of 12 Da.

The mole: counting atoms by weighing them

Atoms are far too small to count one by one, so chemists count them by weighing. A carbon atom has 12 times the mass of a hydrogen atom, so 12 g of carbon holds the same number of atoms as 1 g of hydrogen.

Chemists use a standard batch size: the number of atoms in exactly 12 g of carbon. An amount of any substance that contains that many particles is a mole (mol).

The number itself is 6.022 × 10²³, known as Avogadro’s number. A positive exponent means “multiply by 10 that many times,” so this is about 602 billion trillion. Counting one atom per second, you’d need about a million times the age of the universe to count a mole.

The practical rule is that one mole of an element has a mass in grams equal to its atomic mass. One mole of hydrogen is 1 g, one mole of carbon is 12 g, and one mole of magnesium is 24 g, and each contains 6.022 × 10²³ atoms.

Isotopes: same element, different neutrons

Every atom of an element has the same number of protons, but the number of neutrons can differ. Forms of an element with different numbers of neutrons are isotopes. The small number written at the upper left of the symbol is the total of protons plus neutrons.

• ¹²C, the most common carbon isotope, has 6 protons and 6 neutrons: atomic number 6, atomic mass 12 Da.
• ¹⁴C, a rare isotope, has 6 protons and 8 neutrons: still atomic number 6, but atomic mass 14 Da.

Nearly 99% of the carbon in living things is ¹²C, and the rest is heavier isotopes. So the atomic mass of carbon on the periodic table is slightly more than 12 (about 12.01). Periodic table masses are averages, weighted by how common each isotope is, which is why they’re rarely whole numbers.

Radioisotopes and medicine

Isotopes of an element have the same number of electrons, so they bond in the same ways and have similar chemical properties. Their nuclei, though, can behave very differently.

Many isotopes are unstable: the nucleus breaks down, or decays, giving off radiation (high-energy particles or rays) until it reaches a stable form. These unstable isotopes are radioisotopes. How fast one decays is described by its half-life, the time it takes for half (50%) of a sample to decay.

Radioisotopes at the low levels found in nature are usually harmless. Heavy exposure to radiation, however, can disrupt how cells work and cause cancer (a disease of uncontrolled cell growth) or even death. Medicine turns radiation to good use in both treatment and diagnosis:

• Radiation therapy. Beams of high-energy radiation are aimed at tumors (masses of cancer cells) to kill the cancer cells.
• PET scans. Glucose, a sugar, is the body’s main fuel. Swapping an atom in glucose for radioactive fluorine (¹⁸F, half-life about 110 minutes) makes a traceable version called FDG. Once it’s injected into the blood, organs absorb FDG as if it were ordinary glucose, and a PET (positron-emission tomography) scanner maps where it collects. Cancer cells use much more glucose than normal cells, so tumors show up as bright spots.

Check yourselfCarbon-14 has 6 protons and 8 neutrons. What are its atomic number and atomic mass, and why is it still carbon?

Its atomic number is 6, and its atomic mass is 14 Da. It’s still carbon because its 6 protons define it as carbon. Only its number of neutrons differs from ordinary ¹²C, which makes it an isotope of carbon.