Isotopes and Average Atomic Mass

What Isotopes Are

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the proton count (atomic number) is unchanged, they are still the same element with the same chemistry. Because neutron counts differ, they have different mass numbers.

Classic example — the three isotopes of hydrogen:

• Protium, ¹H: 1 proton, 0 neutrons
• Deuterium, ²H: 1 proton, 1 neutron
• Tritium, ³H: 1 proton, 2 neutrons

All three are hydrogen (1 proton, 1 electron when neutral) and bond the same way, but their masses differ.

Why isotopes behave alike chemically

Chemical behavior is governed by electrons, and isotopes of an element have identical electron arrangements (same atomic number → same electrons). Neutrons live in the nucleus and do not affect bonding. So carbon-12 and carbon-14 react identically; only their mass and nuclear stability differ.

Isotope Notation

The Regents exam writes isotopes two equivalent ways:

• Hyphen notation: element name or symbol, dash, mass number — for example, carbon-14 or C-14.
• Nuclear (AZ) notation: the mass number as a superscript and atomic number as a subscript to the left of the symbol.

From either form you can recover everything:

Notice the protons stay 6 (that is what makes it carbon) while neutrons climb, raising the mass number.

Average Atomic Mass

The atomic mass value printed on the Periodic Table is the weighted average of the masses of all naturally occurring isotopes of that element, weighted by how common each one is (its percent abundance).

This is why most atomic masses are decimals: chlorine's 35.45 u is not the mass of any single chlorine atom — it is the average of chlorine-35 and chlorine-37 weighted by their abundances.

The formula and procedure

Average atomic mass = (mass₁ × abundance₁) + (mass₂ × abundance₂) + …, where each abundance is written as a decimal (divide the percent by 100).

Step by step:

1. Convert each percent abundance to a decimal (e.g., 75% → 0.75).
2. Multiply each isotope's mass by its decimal abundance.
3. Add the products together.
4. The sum is the average atomic mass in atomic mass units (u).

Worked Examples

Example 1 — chlorine. Chlorine-35 (mass 35.0 u) is 75.0% abundant; chlorine-37 (mass 37.0 u) is 25.0% abundant.

• (35.0 × 0.750) + (37.0 × 0.250)
• = 26.25 + 9.25
• = 35.5 u

That matches the ~35.45 u on the Periodic Table.

Example 2 — a two-isotope element. Isotope A: mass 10.0 u, 20.0% abundant. Isotope B: mass 11.0 u, 80.0% abundant.

• (10.0 × 0.200) + (11.0 × 0.800)
• = 2.00 + 8.80
• = 10.8 u

The answer leans toward 11.0 because isotope B is far more abundant — a built-in sanity check.

Sanity-check rule

The weighted average always lands closest to the mass of the most abundant isotope. If your answer is nearer the rare isotope, you swapped the abundances. The average must fall between the lightest and heaviest isotope masses — never outside that range.

Working Backward and Reading Graphs

Regents clusters often supply isotope data in a table or bar graph and ask you to reason from it rather than just plug numbers.

• If a graph shows one tall bar and one short bar, the element's atomic mass will sit near the tall (more abundant) isotope's mass.
• If two isotopes are equally abundant (50%/50%), the average is exactly halfway between their masses.
• If the printed atomic mass is given and you know one isotope's mass and abundance, you can solve for the other abundance because all abundances must sum to 100%.

Worked example: An element has only two isotopes. Mass-20 is 90.0% abundant; the other isotope is mass-22. Its abundance must be 100% − 90.0% = 10.0%, so the average = (20 × 0.900) + (22 × 0.100) = 18.0 + 2.2 = 20.2 u.

Why isotopes still differ

Though isotopes react alike, their nuclear behavior can differ. Some isotopes are radioactive (unstable) and decay, like carbon-14 used in carbon dating, while others are stable, like carbon-12. This nuclear difference does not change chemical bonding but matters in the nuclear-chemistry topics later in the course.

Common Exam Traps

• Forgetting to convert percent to a decimal. Multiplying by 75 instead of 0.75 inflates the answer 100-fold. Always divide percents by 100 first.
• Averaging masses without weighting. A plain (35 + 37) ÷ 2 = 36 ignores abundance and is wrong; you must weight by how common each isotope is.
• Thinking isotopes are different elements. Same protons means same element; only the neutron count and mass differ.
• Confusing mass number with atomic mass. Mass number is a whole-number count of protons + neutrons for one atom; atomic mass is the decimal weighted average across all isotopes.
• Expecting the average to equal a real atom's mass. No single chlorine atom weighs 35.45 u — that value only describes the natural mixture.