Theme E — Nuclear and Quantum Physics
E.3.1 Isotopes and Radioactive Decay — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 18 of 45 1 quiz
Curriculum Equation Key Radioactive Decay & Half-Life FormulasFast Exam Solution
N(t) = N₀ × (1/2)t / t½ | λ = ln(2) / t½ ≈ 0.693 / t½ | E = Δm × c²
Lesson summary
E.3.1 Isotopes and Radioactive Decay — IB PHYSICS SL notes: Describe isotopes, explain why some nuclei are unstable and state the random and spontaneous nature of radioactive decay.Nuclide — a particular type of nucleus, written AZXA is the nucleon (mass) number, Z the proton (at…
- Carbon example
- Nuclear behaviour
- Isotopic data
- Relative atomic mass
- Measurement
- Carbon dating
Part 1 of 8Nuclides and isotopes
Nuclide
- Nuclide a particular type of nucleus, written AZX
- A is the nucleon (mass) number, Z the proton (atomic) number and N = A − Z the neutron number.
- The symbol X is fixed by Z, so the lower number is sometimes dropped.
Isotopes
- Isotopes nuclei with the same number of protons but different numbers of neutrons
- They have a fixed Z and a different A.
- Hydrogen has isotopes with one proton and different numbers of neutrons, such as deuterium and tritium.
Carbon example
- Carbon example carbon-12, carbon-13 and carbon-14 all have Z = 6 with N = 6, 7 and 8
Chemistry
- Chemistry it depends on the electron arrangement, which depends on Z, so isotopes of one element behave almost identically in reactions
Nuclear behaviour
- Nuclear behaviour it can differ dramatically, for example carbon-12 is stable but carbon-14 is not
Part 2 of 8Isotopic data
Isotopic data
- Isotopic data the relative amounts of the different isotopes of an element in a substance
Relative atomic mass
- Relative atomic mass the periodic table value takes into account the masses and abundances of all the naturally occurring isotopes
- It is the sum of mass × relative abundance for each isotope.
- A sample of oxygen with 16O, 17O and 18O in the ratio 0.9976, 0.0004, 0.002 gives 16.00.
Measurement
- Measurement a mass spectrometer gives the percentage abundance of the isotopes in a sample
Carbon dating
- Carbon dating the ratio of stable carbon-12 to unstable carbon-14 in dead tissue is compared with the ratio in living tissue to find its age
Part 3 of 8Why some nuclei are unstable
Competing interactions
- The strong nuclear force attracts neighbouring nucleons over a very short range of about 1–3 fm and is the same between protons and neutrons.
- The electromagnetic force repels every pair of protons and acts over a long range.
Large nuclei
- Large nuclei a proton feels repulsion from all the other protons but attraction only from nearby nucleons
- Too few neutrons, too many neutrons or too many nucleons make the nucleus unstable.
Imbalance
- Imbalance an imbalance of neutrons and protons makes isotopes unstable, so they decay constantly and emit radiation to reach a more stable form
Timescale
- Timescale decay times range from a few nanoseconds to over 100 000 years
Part 4 of 8Line of stability
Graph
- Graph plotting N against Z for stable nuclides gives a narrow band
Light nuclei
- Light nuclei the band follows N = Z
Heavier nuclei
- Heavier nuclei the band curves upward to N greater than Z, because extra neutrons add strong-force attraction without adding repulsion
Part 5 of 8Radioactive decay
Radioactive decay
- Radioactive decay the emission of particles or electromagnetic radiation from an unstable nucleus,
- which becomes a different nuclide (the daughter) or a lower-energy state of the same nuclide
Main emissions
- Main emissions alpha particles, beta particles and gamma photons
Ionising
- Ionising the radiation can knock electrons out of atoms along its path
- This makes it hazardous to living tissue.
- It also lets it be detected, for example in a Geiger–Müller tube.
Part 6 of 8Spontaneous and random decay
Spontaneous
- Spontaneous the decay is not triggered by anything external
- Heating, cooling, high pressure and chemical bonding do not change the chance of decay, because the cause lies inside the nucleus.
Random
- Random it is impossible to predict when a particular nucleus will decay
- Each nucleus has a fixed probability of decaying in any second.
- A nucleus that has survived for a long time is no more due to decay than a new one.
Large samples
- Large samples the randomness averages out into a smooth predictable pattern, giving the exponential law and half-life
Small samples
- Small samples the count rate fluctuates visibly, typically by about the square root of the count
Part 7 of 8Evidence for randomness
Scatter
- Scatter repeated count-rate measurements on a long-lived source at fixed distance scatter about a mean
- The scatter remains after careful control of the experiment.
Graph
- Graph the number of undecayed nuclei against time is smooth only when N is very large
- For a few dozen nuclei it becomes a ragged staircase.
Later quantities
- Later quantities activity is the average number of decays per second and the decay constant is the probability per unit time that a nucleus decays
Part 8 of 8More from the specification
1Radioactive isotope detection
- Radioactive isotope detection measuring characteristic decay half-lives provides a precise analytical means to identify unstable atomic nuclei.
2Isotopes and Radioactive Decay Modes
- Isotopes of an element share the same number of protons but have different numbers of neutrons;
- unstable isotopes undergo spontaneous radioactive decay, emitting penetrating alpha, beta,
- or gamma radiation while nucleon number decreases or atomic number changes.
3Background Radiation and Activity Correction
- Background radiation originates from cosmic rays and natural terrestrial radionuclides;
- to determine the true activity of a radioactive source, background count rate must be subtracted from measured raw detector counts.
4Nuclear Binding Energy and Energy Released
- Nuclear binding energy is the energy required to disassemble a nucleus into its constituent nucleons;
- in spontaneous decay reactions, total mass decreases (mass defect Δm),
- and the energy released is calculated from Einstein's equation E = Δm·c².
5Binding energy
- The minimum energy required to separate the nucleons of a nucleus to infinity.
6Background radiation
- Radiation that is always present in the environment.
7Penetrating power
- How far radiation travels through a material.
8Nuclear notation
- Symbol showing mass number and atomic number.
9Beta-plus decay
- Proton changes to a neutron with emission of a positron and a neutrino.
10Decay equation
- An equation in nuclide notation with balanced nucleon and proton numbers.
Key terms
| Term | Meaning |
|---|---|
| Nuclide | A particular type of nucleus with given Z and N. |
| Isotope | Nuclides of the same element (same Z) with different numbers of neutrons. |
| Isotopic data | The relative amounts of different isotopes of an element in a substance. |
| Spontaneous | Occurring without any external cause. |
| Random | Impossible to predict for an individual nucleus; each has a fixed probability of decay per unit time. |
| Daughter nuclide | The nuclide produced after a decay. |
Avoid these mistakes
1
Believing isotopes have different numbers of protons — they have the same Z and differ in neutrons only.
2
Thinking heat or chemical reaction can speed up or slow down decay — decay is spontaneous.
3
Saying a nucleus that has not decayed for a long time is more likely to decay soon — the probability per unit time is constant.
4
Treating random as unpredictable even on average — the average behaviour of a large sample is very predictable.
5
Confusing nucleon number A with neutron number N — N = A − Z.
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