Fission, Fusion, and Nuclear Decay
Nuclear processes are constrained by conservation laws and mass–energy equivalence; fission and fusion can release energy, while radioactive samples decay probabilistically with rates described by a decay constant and half-life.
Fission, Fusion, and Nuclear Decay: quick answer
Nuclear processes are constrained by conservation laws and mass–energy equivalence; fission and fusion can release energy, while radioactive samples decay probabilistically with rates described by a decay constant and half-life. Unit 15.7 combines two scales of reasoning: individual nuclear reactions obey conservation laws, while a finite population of unstable nuclei is described statistically. Keep those two ideas separate—mass–energy/reaction bookkeeping for one process and exponential probability for a sample.
Use the current radioactive-decay definition: a nucleus may transform into different nucleus/nuclei or move to a lower energy level of the same nucleus. Do not predict an individual nucleus’s exact decay time from half-life.
What you should be able to explain and do
Use these as closed-note retrieval prompts before the worked reasoning.
Apply conservation of nucleon number, energy and momentum to a nuclear process.
Use mass–energy equivalence to relate a rest-mass change to energy released or required.
Relate decay constant to half-life and compare decay rates.
Use exponential/half-life relationships to determine remaining population or infer elapsed time while recognizing the probabilistic meaning.
Terms you need before using the model
Important vocabulary is defined here so the lesson does not depend on an unexplained internal-link jump.
strong force
the short-range interaction that dominates nucleon interactions at nuclear scales
nucleon number
the total number of protons and neutrons, conserved in the nuclear-reaction bookkeeping used here
fission
splitting of a nucleus into two or more smaller nuclei plus possible subatomic particles
fusion
combination of two or more smaller nuclei into a larger nucleus plus possible subatomic particles
radioactive decay
spontaneous transformation of a nucleus into one or more different nuclei, or to a lower energy level of the same nucleus
half-life
the time required for half of the initial radioactive nuclei in a sample to have decayed statistically
decay constant
the probability-rate parameter λ that characterizes exponential radioactive decay of a sample
Keep variables, conditions and physical meaning together
Select the relationship only after identifying the physical model and representation.
| Relationship | Variables / meaning | Use when | Physical interpretation |
|---|---|---|---|
ΔE = Δmc² | ΔE change in rest-mass energy (J); Δm mass difference (kg); c speed of light (m/s) | nuclear reactions/processes where rest mass and other energy forms are exchanged | a small decrease in total rest mass can appear as kinetic energy of products and/or photon energy |
λ = ln(2)/t1/2 | λ decay constant (s⁻¹); t1/2 half-life (s) | connecting the exponential decay rate to half-life | a shorter half-life corresponds to a larger decay constant |
N = N0e^(−λt) = N0(1/2)^(t/t1/2) | N remaining radioactive nuclei; N0 initial nuclei; λ decay constant (s⁻¹); t time; t1/2 half-life | statistical population decay or age/remaining-fraction calculations | after three half-lives the expected remaining population is N0/8 |
Turn evidence into physics
Move physical situation ↔ diagram/graph/equation ↔ verbal claim without losing the model boundary.
Reaction bookkeeping: show reactants → products and check nucleon number plus energy/momentum conservation.
Mass–energy bar: a decrease in total rest-mass energy appears as product kinetic energy and/or photons.
Decay graph: N versus t is exponential, while lnN versus t is linear with slope −λ.
Half-life markers: equal time intervals multiply the remaining population by 1/2 rather than subtracting a fixed amount.
Change one condition and inspect what responds
Predict first, then move a control. The tool stays inside the topic model.
Two examples with model selection exposed
The point is the reasoning path, not only the final number.
Half-life population
Situation: A sample begins with 8000 radioactive nuclei and has half-life 6.0 h. How many are expected after 18 h?
Reasoning: 18 h is three half-lives, so multiply by (1/2)³.
Result: N=8000/8=1000 nuclei expected statistically.
Mass–energy release
Situation: A nuclear process reduces total rest mass by 2.0×10⁻²⁹ kg. Estimate the released energy.
Reasoning: Use ΔE=Δmc² with c≈3.00×10⁸ m/s.
Result: ΔE≈1.8×10⁻¹² J, appearing in other energy forms while total energy remains conserved.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 15.7?
Use nuclear energy/decay-population reasoning when rest-mass changes release energy or when a radioactive sample changes statistically over time.
How this idea fits the course
Mass-energy and population decay set up the reaction bookkeeping and specific decay modes classified in 15.8.
Scope check before solving
Use the current radioactive-decay definition: a nucleus may transform into different nucleus/nuclei or move to a lower energy level of the same nucleus. Do not predict an individual nucleus’s exact decay time from half-life.
How would the evidence test the model?
Identify what changes, what is measured, the graph/representation that tests the relationship, and the uncertainty that matters.
Errors to remove before more practice
Repair the model or representation decision before doing extra arithmetic.
Predicting an exact decay time for one nucleus
Half-life and λ describe probabilities/populations, not the exact future of a single nucleus.
Subtracting the same number each half-life
Exponential decay removes the same fraction, not the same absolute number.
Saying mass is separately conserved in nuclear reactions
Total energy is conserved; rest mass can be exchanged with other energy forms through E=mc².
Restricting radioactive decay to changing element identity
A radioactive transition can also take a nucleus to a lower energy level of the same nucleus.
Six checks before moving on
Close the notes and test transfer before switching to the separate practice pages.
- I can define every important term used in this lesson.
- I can choose the model before selecting an equation.
- I can translate between the key representation and a verbal prediction.
- I can state the relationship conditions and scope boundary.
- I can design or interpret evidence that tests the model.
- I can explain the topic without relying on question-pattern memorization.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 15.7 FAQs
What is conserved in nuclear reactions?
Use the relevant conservation laws including nucleon number, total energy and momentum; charge is also tracked in nuclear bookkeeping.
What is half-life?
The time for half of an initial radioactive population to have decayed statistically.
Can half-life predict when one nucleus will decay?
No. Individual decay time is indeterminable; the sample behavior is probabilistic.
How are λ and half-life related?
λ=ln2/t1/2.
What changed in the current decay wording?
Radioactive decay includes spontaneous transformation into different nucleus/nuclei or transition to a lower energy level of the same nucleus.