Isotopes, Isobars, Isotones

Atoms of the same element always have the same number of protons (atomic number, Z), but they can differ in the number of neutrons in their nucleus. This variation gives rise to isotopes — atoms that share the same atomic number but have different mass numbers. Understanding isotopes is essential for explaining why the atomic masses listed on the periodic table are rarely whole numbers, and why different atoms of the same element can behave identically in chemical reactions yet differ in nuclear stability and mass. Beyond isotopes, chemists and nuclear physicists also identify two other important nuclear relationships: isobars, which are atoms of different elements that share the same mass number (A), and isotones, which are atoms of different elements that share the same number of neutrons (n). These three concepts — isotopes, isobars, and isotones — form the foundation of nuclear chemistry and help us understand radioactive decay, nuclear reactions, and the stability of atomic nuclei. The existence of isotopes directly explains why atomic masses are weighted averages rather than whole numbers. For example, chlorine has two naturally occurring isotopes — chlorine-35 and chlorine-37 — present in nature in specific proportions. The average atomic mass of chlorine (approximately 35.45 u) reflects this natural abundance. Mastering these concepts allows students to calculate average atomic masses, interpret mass spectrometry data, and understand how nuclear medicine uses specific isotopes for diagnostics and treatment.

Key takeaways
  • Key Notation: Mass Number and Atomic Number
  • Isotopes — Same Z, Different A
  • Isobars — Same A, Different Z
  • Isotones — Same n, Different Z and A
  • Average Atomic Mass — Weighted Average of Isotopes

Key Notation: Mass Number and Atomic Number

Every nuclide (a specific nuclear species) is written as ZAX^{A}_{Z}\text{X}, where X is the element symbol, A is the mass number (protons + neutrons), and Z is the atomic number (number of protons). The number of neutrons is found by: n = A − Z. For example, 612C^{12}_{6}\text{C} has 6 protons and 6 neutrons, while 614C^{14}_{6}\text{C} has 6 protons and 8 neutrons.

Isotopes — Same Z, Different A

Isotopes are atoms of the same element (same Z, same number of protons) that have different numbers of neutrons, giving them different mass numbers. Because chemical behaviour is determined by electron configuration — and electrons equal protons in a neutral atom — isotopes are chemically nearly identical. Examples: 11H^{1}_{1}\text{H} (protium), 12H^{2}_{1}\text{H} (deuterium), and 13H^{3}_{1}\text{H} (tritium) are the three isotopes of hydrogen. All have Z = 1 but A = 1, 2, and 3 respectively. Similarly, 92235U^{235}_{92}\text{U} and 92238U^{238}_{92}\text{U} are uranium isotopes — the former is fissile and used in nuclear reactors, while the latter is far more abundant in nature.

Isobars — Same A, Different Z

Isobars are atoms of different elements that share the same mass number (A) but have different atomic numbers (Z) and therefore different numbers of protons and neutrons. They are NOT the same element and have completely different chemical properties. Example: 1840Ar^{40}_{18}\text{Ar} (18 protons, 22 neutrons) and 2040Ca^{40}_{20}\text{Ca} (20 protons, 20 neutrons) are isobars — both have A = 40 but are entirely different elements (argon and calcium). Another classic pair: 614C^{14}_{6}\text{C} and 714N^{14}_{7}\text{N} share A = 14.

Isotones — Same n, Different Z and A

Isotones are atoms of different elements that have the same number of neutrons (n = A − Z), but different atomic numbers and mass numbers. Example: 614C^{14}_{6}\text{C} has n = 14 − 6 = 8 neutrons, and 715N^{15}_{7}\text{N} also has n = 15 − 7 = 8 neutrons. These are isotones. Another pair: 2040Ca^{40}_{20}\text{Ca} and 1939K^{39}_{19}\text{K} both have 20 neutrons (40Ca^{40}\text{Ca}: 40−20=20; 39K^{39}\text{K}: 39−19=20). Isotones share similar nuclear shell structures because nuclear stability depends on neutron number.

Average Atomic Mass — Weighted Average of Isotopes

The atomic mass shown on the periodic table is the weighted average atomic mass, calculated from the masses and natural abundances of all naturally occurring isotopes of an element. The formula is: mˉ=∑i(fractional abundancei×massi)\bar{m} = \sum_i (\text{fractional abundance}_i \times \text{mass}_i). For chlorine: 35Cl^{35}\text{Cl} has mass 34.969 u and abundance 75.77%, while 37Cl^{37}\text{Cl} has mass 36.966 u and abundance 24.23%. Average = (0.7577 × 34.969) + (0.2423 × 36.966) = 26.496 + 8.957 = 35.453 u ≈ 35.45 u. This is why chlorine's atomic mass is not a whole number.

The Key Equation

mˉ=∑i(fi×mi)\bar{m} = \sum_{i} (f_i \times m_i)
  • \bar{m} — Average atomic mass (atomic mass units (u) or g/mol): The weighted average mass of all naturally occurring isotopes of an element, as listed on the periodic table.
  • f_i — Fractional abundance of isotope i (dimensionless (decimal fraction)): The proportion of atoms in a natural sample that are isotope i; expressed as a decimal (e.g., 75.77% = 0.7577). All fractional abundances must sum to 1.
  • m_i — Isotopic mass of isotope i (atomic mass units (u)): The actual mass of a single atom of isotope i, measured relative to 1/12 the mass of a carbon-12 atom. Slightly different from the mass number due to nuclear binding energy.

Worked Example

Problem. Boron has two naturally occurring isotopes: boron-10 (510B^{10}_{5}\text{B}) with isotopic mass 10.013 u and natural abundance 19.9%, and boron-11 (511B^{11}_{5}\text{B}) with isotopic mass 11.009 u and natural abundance 80.1%. (a) Calculate the average atomic mass of boron. (b) Identify a nuclide that is an isobar of 510B^{10}_{5}\text{B}. (c) Identify a nuclide that is an isotone of 511B^{11}_{5}\text{B}.

mˉ(B)=(0.199×10.013)+(0.801×11.009)=10.811 u\bar{m}(\text{B}) = (0.199 \times 10.013) + (0.801 \times 11.009) = 10.811\,\text{u}

Answer. Average atomic mass of boron = 10.811 u; Isobar of B-10: beryllium-10; Isotone of B-11: carbon-12

Figure
Diagram
Isotopes, Isobars, and Isotones of Selected NuclidesISOTOPES (same Z)Same element, same ZDifferent A, different n¹H ²H ³HZ=1 Z=1 Z=1n=0 n=1 n=2All are hydrogenISOBARS (same A)Different element, diff ZSame A, different n⁴⁰Ar ⁴⁰K ⁴⁰CaZ=18 Z=19 Z=20n=22 n=21 n=20All have A = 40ISOTONES (same n)Different element, diff ZDifferent A, same n¹⁴C ¹⁵N ¹⁶OZ=6 Z=7 Z=8n=8 n=8 n=8All have n = 8Average Atomic Mass: Chlorine Example³⁵Clmass: 34.969 uabundance:75.77%³⁷Clmass: 36.966 uabundance:24.23%+Average Mass= 0.7577×34.969+ 0.2423×36.966= 35.45 u=Summary: Z = protons, A = Z + n (mass number), n = neutrons = A − Z
Origins · 1 minFrederick Soddy and how this was discovered
FS
Frederick Soddy
1877–1956 · British

Frederick Soddy coined the term 'isotope' in 1913, derived from the Greek words 'isos' (equal) and 'topos' (place), meaning 'same place' — referring to elements that occupy the same position on the periodic table yet have different atomic masses. Working with Ernest Rutherford, he helped discover radioactive transmutation, showing that radioactive decay converts one element into another. He also formulated the radioactive displacement law (the Fajans-Soddy rules) describing how alpha and beta decay change an atom's position on the periodic table. Soddy was awarded the Nobel Prize in Chemistry in 1921 for his work on radioactive substances and isotopes. Soddy was also an unconventional economist: he wrote extensively about how the physics of energy should reform economic theory, arguing decades before modern environmental economics that infinite economic growth on a finite planet was physically impossible.

  • Atomic Number and Mass Number — Isotopes, isobars, and isotones are all defined by the relationship between Z (atomic number) and A (mass number); understanding these two quantities is a prerequisite.
  • Radioactive Decay — Many isotopes are radioactive and decay by alpha, beta, or gamma emission, transforming one nuclide into an isobar or a different nuclide. Understanding isotopes is essential for studying nuclear stability and decay series.
  • Mass Spectrometry — Mass spectrometers directly measure the masses and relative abundances of isotopes, providing the data used to calculate average atomic masses as discussed in this concept.
  • Nuclear Binding Energy and Mass Defect — The isotopic masses used in average atomic mass calculations differ slightly from whole numbers due to the binding energy that holds the nucleus together — a concept explained by Einstein's mass-energy equivalence.