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Half-life used to be a standard board and entrance topic. It has quietly moved. If you are preparing from older books or older question banks, you may spend hours on decay problems your exam no longer asks, or skip them when your exam still does. This post sets out where radioactive decay stands in the 2026 syllabi, then works through the maths for students who need it.
Which exams still include radioactive decay?
Here is what the official documents for 2026 say:
JEE (Advanced). The 2026 information brochure lists "α, β and γ radiations; Law of radioactive decay; Decay constant; Half-life and mean life" under Modern Physics.
JEE (Main). The NTA syllabus for 2026 lists, under Atoms and Nuclei, the composition and size of the nucleus, mass defect, binding energy, and fission and fusion. It does not list radioactive decay or half-life.
NEET (UG). The NEET (UG) 2026 syllabus has the same Atoms and Nuclei unit, also without decay.
CBSE Class 12. The CBSE physics curriculum for 2026-27 lists, for the Nuclei chapter, composition and size of the nucleus, nuclear force, mass-energy relation, mass defect, binding energy, fission and fusion.
The current NCERT chapter Nuclei (2026-27 reprint) still names the three kinds of decay in a short section, but gives no decay law. Syllabi change every year, so read the official document for your exam and year before you plan. In chemistry, the same exponential maths is still in both the JEE (Main) and NEET syllabi as the half-life of first-order reactions, so the skills below are not wasted.
What does the decay law say?
Each nucleus has a fixed probability per unit time of decaying, called the decay constant λ. For a large number of nuclei, the rate of decay is proportional to the number present, dN/dt = −λN, which gives:
N = N₀e^(−λt)
Half-life: T½ = ln 2/λ ≈ 0.693/λ
Mean life: τ = 1/λ = T½/ln 2 ≈ 1.44 T½
Activity: A = λN, which falls with the same half-life as N.
A useful form when t is a multiple of T½: N/N₀ = (½)^(t/T½).
Worked examples
Take a sample with a half-life of 8.0 days.
After 24 days, t/T½ = 3, so N/N₀ = (½)³ = 1/8. Seven-eighths has decayed.
After 12 days, t/T½ = 1.5, so N/N₀ = (½)^1.5 ≈ 0.354.
Time for 90% to decay. N/N₀ = 0.10, so t = ln 10/λ = T½ × (ln 10/ln 2) ≈ 8.0 × 3.32 ≈ 26.6 days.
Mean life. τ = 8.0/0.693 ≈ 11.5 days.
Activity. For N = 1.0 × 10²⁰ nuclei: T½ = 8.0 × 86400 = 6.91 × 10⁵ s, so λ = 0.693/(6.91 × 10⁵) ≈ 1.0 × 10⁻⁶ s⁻¹ and A = λN ≈ 1.0 × 10¹⁴ Bq.
Which mistakes cost marks?
Thinking two half-lives empties the sample. See the callout.
Mixing half-life and mean life. τ is about 1.44 times T½, not equal to it.
Using log₁₀ where ln is needed. ln 2 ≈ 0.693; log₁₀ 2 ≈ 0.301. Keep track of which you use.
Mismatched units. If λ is in s⁻¹, time must be in seconds. Convert days before calculating activity.
Thinking half-life depends on the amount. It is a property of the nucleus, the same for a gram or a tonne.
There is a conceptual trap too. Prather (2005) studied students' ideas about radiation and found they were often unable to tell irradiation from contamination, and that many reasoning difficulties about decay and half-life came from inaccurate mental models of the atom. If decay feels like a formula with no picture behind it, revisit the structure of the nucleus first.
If you are revising this alongside chemistry, our post on chemical kinetics and rate laws shows the same exponential working. To see how the two JEE papers differ more broadly, read JEE Main vs JEE Advanced.
If you are not sure which topics your own exam includes and where to start, Fermi's AI tutor can work out what you already know and build a plan for the session, so you spend time on what is actually tested.
A practice routine for students who need it
Day 1: Derive N = N₀e^(−λt) from dN/dt = −λN, then find T½ and τ.
Day 2: Eight numerical problems: fractions left, time for a given fraction, activity.
Day 3: Three graph questions: read T½ from a plot of N or ln N against time.
Day 4: A mixed set with nuclear binding energy and first-order kinetics questions.
Before your next revision session, open your exam's current syllabus PDF and confirm whether radioactive decay is on it.
