Atomic Mass & Number
Isotopes, Relative Atomic Mass, Atomic Number & Calculations
Quick Review
In Lesson 1.5 we introduced the three subatomic particles and the concepts of atomic number and mass number. This lesson builds directly on those foundations, going deeper into how atomic masses are measured, what isotopes mean for real-world chemistry, and how to perform calculations using the periodic table.
Atomic Mass Units
Atoms are so small that measuring their masses in grams would produce inconveniently tiny numbers. Instead, chemists use the atomic mass unit (amu), also written as u or Da (dalton).
The atomic mass unit is defined as exactly 1/12 of the mass of a carbon-12 atom. This standard was chosen because carbon-12 is abundant, stable, and easily measured. On this scale, one proton and one neutron each have a mass of approximately 1 amu, while an electron has a mass of only 0.000549 amu — negligible for most calculations.
A unit of mass equal to 1/12 the mass of one carbon-12 atom. Approximately 1.661 × 10⁻²⁷ kg. Used to express the masses of atoms and subatomic particles.
Mass number (A) is always a whole number — it counts protons + neutrons. Atomic mass is a decimal value in amu — it reflects the weighted average of all isotopes.
An electron has a mass of 9.109 × 10⁻³¹ kg — about 1836 times lighter than a proton. For nearly all chemistry calculations, electron mass is so small it can be ignored without meaningful error. The mass of an atom is essentially the mass of its protons and neutrons.
Isotopes in Depth
Most elements in nature exist as a mixture of isotopes. Each isotope has the same atomic number (same element) but a different mass number (different neutron count). The proportion of each isotope in a natural sample is called its natural abundance, expressed as a percentage.
Natural abundances are remarkably consistent — a sample of carbon from coal, diamond, human tissue, or a distant meteorite all contain approximately the same ratio of carbon-12 to carbon-13.
Some isotopes are unstable — their nuclei contain an imbalanced ratio of protons to neutrons and decay over time, emitting radiation. These are called radioisotopes. Carbon-14 (used in radiocarbon dating), iodine-131 (used in thyroid cancer treatment), and uranium-235 (nuclear fuel) are important examples. Stable isotopes do not decay.
Relative Atomic Mass
Because most elements exist as mixtures of isotopes, the mass shown on the periodic table is not the mass of any single isotope — it is the relative atomic mass (also called standard atomic weight), which is the weighted average of all naturally occurring isotopes.
A weighted average gives more influence to isotopes that are more abundant. If one isotope makes up 99% of a sample, the average will be very close to its mass.
Where fractional abundance = percentage ÷ 100. Sum over all naturally occurring isotopes of the element.
This is why chlorine has an atomic mass of approximately 35.5 on the periodic table — not 35 or 37. It is the weighted average of ³⁵Cl (75.77%) and ³⁷Cl (24.23%), landing between the two values but closer to 35 because it predominates.
Step-by-Step Calculations
Calculating weighted average atomic mass follows a consistent method. Here is the general approach broken into explicit steps.
Divide each isotope’s percentage abundance by 100 to get its fractional abundance.
This gives each isotope’s contribution to the average.
Add together the contributions from all isotopes.
The result should lie between the lightest and heaviest isotope masses, closer to the most abundant one. Compare to the periodic table value.
Using the Periodic Table for Mass Data
The periodic table gives you all the atomic number and mass data you need for calculations. Understanding what each number means — and what it doesn’t mean — prevents common errors.
Always a whole number. Never changes for a given element. Use this to find protons, and (for neutral atoms) electrons. Found above the symbol in most periodic tables.
Usually a decimal. This is the weighted average — not a single isotope’s mass. Use this in mole calculations and stoichiometry. Found below the symbol in most periodic tables.
Always a whole number. Specific to a particular isotope (e.g. ¹²C or ¹⁴C). Use this when calculating neutrons: N = A − Z. Not shown directly on periodic tables.
N = A − Z. Not shown on the periodic table — you always calculate it. Can vary between isotopes of the same element while Z stays constant.
Students often confuse the relative atomic mass (decimal, periodic table value) with the mass number (whole number, specific to one isotope). You cannot calculate neutrons using the decimal atomic mass — you need the mass number of the specific isotope being described. Always identify which number is being given in a question before calculating.
Worked Examples
Step 1: Convert to fractional abundances: 19.9% → 0.199; 80.1% → 0.801
Contribution of ¹¹B = 11.009 × 0.801 = 8.8182
Ar = 1.9926 + 8.8182 = 10.811 amu
This matches the periodic table value for boron (10.81). The result is closer to 11 because ¹¹B is the more abundant isotope (80.1%).
Method: Let the fractional abundance of ⁶⁹Ga = x. Then ⁷¹Ga = (1 − x). Set up the weighted average equation.
68.926x + 70.925 − 70.925x = 69.723
−1.999x = 69.723 − 70.925 = −1.202
x = −1.202 ÷ −1.999 = 0.6013
⁶⁹Ga: 60.1% | ⁷¹Ga: 39.9%
Practice Questions
Q1. The relative atomic mass of an element shown on the periodic table is best described as:
Q2. An atom of ⁵⁹Co (cobalt, Z = 27) has how many neutrons?
Q3. Silicon has three isotopes: ²⁸Si (92.23%), ²⁹Si (4.67%), and ³⁰Si (3.10%). Its relative atomic mass will be closest to:
Q4. A ³⁴S²⁻ ion (sulfur, Z = 16) has how many electrons?
Q5. Magnesium has three isotopes with masses ~24, ~25, and ~26 amu. The periodic table lists magnesium’s atomic mass as 24.305. This tells you that:
Key Takeaways
- The atomic mass unit (amu) = 1/12 the mass of ¹²C. Protons and neutrons each have a mass of ~1 amu; electrons are negligible.
- Atomic number (Z) = protons. Mass number (A) = protons + neutrons. Neutrons = A − Z.
- Isotopes are atoms of the same element with different neutron counts and mass numbers but identical chemical behaviour.
- Natural abundance is the percentage of each isotope found in a naturally occurring sample — consistent worldwide.
- Relative atomic mass (Ar) on the periodic table is the weighted average of all naturally occurring isotopes: Ar = Σ(mass × fractional abundance).
- The weighted average lies between isotope masses, pulled toward the most abundant isotope.
- For ions: electrons = Z ± charge. Adding electrons (anion) makes the charge negative; removing electrons (cation) makes it positive.