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Every chemistry student now learns that carbon-12 and carbon-14 are the same element with different masses. A little over a century ago that idea sounded impossible: an element was supposed to have one atomic weight. Frederick Soddy, working with radioactive substances, showed it was wrong. This post covers what he found, the displacement law, a worked decay chain and what his way of working can teach you.
Who was Frederick Soddy?
The Nobel Prize biography gives the outline. Soddy was born in Eastbourne, England, on 2 September 1877 and graduated from Oxford in chemistry in 1898. From 1900 to 1902 he worked at McGill University in Montreal with Ernest Rutherford. Together they concluded that radioactivity involves atoms breaking up and forming new kinds of matter. In London he then worked with William Ramsay and showed by spectroscopy that helium is produced when radium decays.
From 1904 to 1914 Soddy lectured at the University of Glasgow. That is where he did the chemical work that led to the displacement law and, in 1913, to the idea of isotopes. The Nobel Prize facts page gives the motivation for his 1921 Chemistry prize: "for his contributions to our knowledge of the chemistry of radioactive substances, and his investigations into the origin and nature of isotopes". He received it a year later, in 1922. He died in Brighton on 22 September 1956.
What puzzle was Soddy trying to solve?
By 1910 chemists had found dozens of new radioactive "elements" in the decay chains of uranium and thorium, far more than the empty boxes in the periodic table. Some of them refused to separate from known elements. In his Nobel lecture, Soddy quotes a 1907 finding by the chemist McCoy and a co-worker that radiothorium was "entirely inseparable from thorium by chemical processes", even though the two had very different radioactive behaviour. He calls this the first definite statement of what we now call isotopes.
His explanation, in his own words in that lecture: "Put colloquially, their atoms have identical outsides but different insides." Chemistry depends on the outer electrons. Radioactive change happens in the nucleus.
What is the radioactive displacement law?
Soddy's lecture sets out the rule that he and Kasimir Fajans, working in Karlsruhe, published independently in early 1913. Each alpha particle expelled "causes a shift of two places in the direction of diminishing mass", and each beta particle "causes a shift of one place in the opposite direction". He also credits Alexander Russell and George de Hevesy, whose partly correct versions came weeks earlier, and Alexander Fleck, whose chemical tests supplied the evidence.
In today's notation, with Z as atomic number and A as mass number:
Alpha decay: Z goes down by 2, A goes down by 4.
Beta (minus) decay: Z goes up by 1, A stays the same.
The rule had a striking prediction. All three natural decay series had to end on lead. Soddy's lecture notes that lead from the thorium series should have atomic weight 208, lead from the uranium series 206, and ordinary lead, at 207.2, "might well be a mixture of both". Measured values backed this up: the lecture reports 207.9 for "thorium-lead" and as low as 206.05 for "uranium-lead".
Why is it called an isotope?
Soddy coined the word in a 1913 letter to Nature, Intra-atomic charge. The NCERT Class 12 chapter Nuclei explains the meaning: in Greek, isotope means "the same place", because isotopes occupy the same place in the periodic table. The same chapter gives chlorine as an example, a mixture of isotopes with masses 34.98 u and 36.98 u.
Worked example: how many decays turn uranium-238 into lead-206?
Uranium-238 has Z = 92. Lead-206 has Z = 82. Find the number of alpha (x) and beta (y) decays.
Use the mass number first. Only alpha decay changes A, by 4 each time. 238 − 206 = 32, so x = 32 ÷ 4 = 8.
Track the atomic number. Eight alpha decays lower Z by 8 × 2 = 16, giving 92 − 16 = 76.
Close the gap with beta decays. Lead needs Z = 82, so y = 82 − 76 = 6.
Check: Z = 92 − 16 + 6 = 82 and A = 238 − 32 = 206. Both match.
For thorium-232 (Z = 90) to lead-208 you should get 6 alpha and 4 beta decays.
What mistakes do students make with decay chains?
Starting with the atomic number. Z is changed by both kinds of decay, so you cannot solve for either from Z alone. Start with A, which only alpha decay changes.
Moving beta decay the wrong way. A beta-minus particle leaves when a neutron becomes a proton, so Z rises by one. Write the equation out until this is automatic.
Thinking isotopes differ chemically. They differ in mass and in nuclear stability, not in how they react.
Exam note: the JEE (Advanced) 2026 brochure lists alpha, beta and gamma radiations and the law of radioactive decay under modern physics, while the JEE (Main) 2026 syllabus lists nuclear composition, mass defect and binding energy but not decay chains. Check the current year's documents before you plan. Our post on where radioactive decay sits in the 2026 syllabi has the details.
What can a student take from how Soddy worked?
Take the stubborn result seriously. Substances that would not separate looked like failed chemistry. Soddy treated the failure as data.
Keep the experiment honest. His lecture says he "scrupulously avoided" thinking about Fleck's results until they were complete, to avoid biasing the work.
Give credit widely. Soddy names Fajans, Russell, Hevesy and Fleck in his own Nobel lecture.
Test the prediction. The lead atomic weights turned a neat rule into accepted science.
A short practice routine: write three decay chains from memory, solve each for alpha and beta counts using the A-first method, then write one sentence on why two isotopes behave alike in a reaction. If the link between protons, neutrons and the periodic table still feels shaky, the Fermi Concept Library covers every concept in physics and chemistry, so you can revise nuclear composition before you return to decay problems.
Next step: solve the thorium-232 chain above on paper, then check your answer against the method.
