Relative isotopic mass

Relative isotopic mass is the mass of an atom of one particular isotope, compared with one twelfth of the mass of an atom of carbon-12. It applies to a single isotope, such as gallium-69, whose relative isotopic mass is 68.926. It is not the same as relative atomic mass, which is the weighted mean of all of an element's isotopes: for gallium, 69.723.

Relative isotopic mass definition

OCR A's A-level specification requires the definitions and gives them in brackets: relative isotopic mass is mass compared with 1/12th mass of carbon-12, and relative atomic mass is weighted mean mass compared with 1/12th mass of carbon-12. Cambridge International defines the same terms using the unified atomic mass unit, which is 1/12 of a carbon-12 atom's mass.

Because it compares one mass with another, relative isotopic mass has no units. Carbon-12 is the standard, so its relative isotopic mass is exactly 12 by definition.

Relative isotopic mass vs relative atomic mass

The gallium values are from NIST. Relative isotopic mass is close to the mass number, but not equal to it. Relative atomic mass sits between the isotopic masses, nearer the more common isotope. More on Ar is in what is relative atomic mass.

Why isn't relative isotopic mass a whole number?

Two things stop the values being whole numbers. Protons and neutrons don't each have a mass of exactly 1 on this scale, and when a nucleus forms, a little mass is converted into binding energy, a different amount for each nucleus. The physics behind this is in mass defect and binding energy. In most chemistry calculations the mass number is close enough, but precise work uses the real isotopic masses.

Measuring it: mass spectrometry

AQA's specification says the mass spectrometer gives accurate information about relative isotopic mass and about the relative abundance of isotopes. In a time-of-flight instrument, AQA lists the stages as ionisation, acceleration to give all ions constant kinetic energy, ion drift, ion detection and data analysis. Lighter ions travel faster, so they reach the detector first.

The spectrum plots abundance against mass to charge ratio, m/z. For ions with a single positive charge, m/z equals the relative isotopic mass, so each peak is one isotope and its height shows how common it is. This is rubidium:

Worked examples

Example 1: Ar from relative isotopic masses

Use the rubidium spectrum to find the relative atomic mass of rubidium, first with the precise relative isotopic masses, then with mass numbers.

1. Multiply each relative isotopic mass by its abundance, add, and divide by the total abundance (100).
2. Precise: (84.912 × 72.17 + 86.909 × 27.83) ÷ 100 = 85.468, which matches NIST's standard atomic weight of 85.4678.
3. With mass numbers: (85 × 72.17 + 87 × 27.83) ÷ 100 = 85.56.
4. Using mass numbers is out by about 0.09 here. That's why data tables of relative isotopic mass, not mass numbers, are used for precise values.

Try a weighted mean yourself, then press Mark to check it in the atomic structure course.

Example 2: finding an abundance

Gallium's relative atomic mass is 69.723. Its isotopes have relative isotopic masses 68.926 and 70.925. Find the percentage of gallium-69.

1. Let the fraction of gallium-69 be x, so the fraction of gallium-71 is 1 − x.
2. 68.926x + 70.925(1 − x) = 69.723.
3. 70.925 − 1.999x = 69.723, so 1.999x = 1.202 and x = 0.601.
4. So 60.1% of gallium atoms are gallium-69, which matches NIST's 60.108%.

Common mistakes

• Mixing up isotopic mass and atomic mass. Relative isotopic mass is for one isotope; relative atomic mass is the weighted mean of all of them.
• Leaving out carbon-12. Both definitions are measured against carbon-12; say so.
• Saying "average" without "weighted". Ar is a weighted mean, weighted by abundance.
• Giving units. Relative masses have none. Grams per mole belongs to molar mass.
• Assuming relative isotopic mass equals the mass number. It is close, but only carbon-12 is exact.

Atomic structure starts the first year of A-level Chemistry, so try today's A-level Chemistry: Year 1 short timed paper. Build isotopes in the Atom Builder to see how only the neutron number changes.

Read next

Chemistry · Atoms and the periodic tableWhat is relative atomic mass? Definition and calculationRelative atomic mass is the weighted average mass of an element's atoms compared with carbon-12. The definition and how to calculate it from isotopes.