Radioactivity IB DP Physics Study Notes - 2025 Syllabus
Radioactivity IB DP Physics Study Notes
Radioactivity IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand
- the changes in the state of the nucleus following alpha, beta and gamma radioactive decay
- the radioactive decay equations involving α, β$^−$, β$^+$, γ
- the existence of neutrinos ν and antineutrinos ν
- the penetration and ionizing ability of alpha particles, beta particles and gamma rays
- that the spectrum of alpha and gamma radiations provides evidence for discrete nuclear energy levels
- the continuous spectrum of beta decay as evidence for the neutrino
- the decay constant λ and the radioactive decay law as given by N = N0e−λt
- that the decay constant approximates the probability of decay in unit time only in the limit of sufficiently small λt
- the activity as the rate of decay as given by A = λN = λN0e−λt the relationship between half-life and the decay constant as given by $T_{\frac{1}{2}} =\frac{ ln2}{λ} $.
Standard level and higher level: 7 hours
Additional higher level: 5 hours
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
Radioactive Decay
- In 1898, Pierre and Marie Curie announced the discovery of two radioactive elements, radium and polonium.
- When these elements were placed near a radio receiver, the receiver picked up some sort of activity coming from the elements.
FYI
Studies showed this radioactivity was not affected by normal physical and chemical processes.
- In 1896, while studying a uranium compound, French scientist Henri Becquerel discovered that a nearby photographic plate had been exposed to some source of “light,” even though it had not been uncovered.
- Apparently, the darkening of the film was caused by a new type of radiation emitted by the uranium compound.
- This radiation had sufficient energy to pass through the cardboard storage box and the glass of the photographic plates.
Alpha particles, beta particles and gamma rays
- Studies revealed three types of radioactive particles.
- If a radioactive substance is placed in a lead chamber and its emitted particles pass through a magnetic field, the three different types of radiation can be distinguished:
- Alpha Particles (α): Two protons (+) and two neutrons (0), identical to a helium nucleus \(_4He\).
- Beta Particles (β): Electrons (-) emitted from the nucleus.
- Gamma Rays (γ): Photons with no charge.
Alpha particles, beta particles and gamma rays

- When a nucleus emits an alpha particle (\(\alpha\)) it loses two protons and two neutrons.
- All alpha particles consistently have an energy of about 5 MeV.
- The decay just shown has the form
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- Since the energy needed to knock electrons off of atoms is just about 10 eV, one alpha particle can ionize a lot of atoms.
- It is just this ionization process that harms living tissue, and is much like burning at the cell level.

- In (\(\beta^-\)) decay, a neutron becomes a proton and an electron is emitted from the nucleus.
- In (\(\beta^+\)) decay, a proton becomes a neutron and a positron is emitted from the nucleus.
- In short, a beta particle is either an electron or it is an anti-electron.
Radioactivity – gamma decay (\(\gamma\))
Recall that electrons in an atom moving from an excited state to a de-excited state release a photon.
Nuclei can also have excited states.
When a nucleus de-excites, it also releases a photon. This process is called gamma (\(\gamma\)) decay.
Thus gamma decay is evidence that just as the atom has discrete energy levels, so, too, does the nucleus.
Absorption Characteristics of Radiation
- Alpha Particles: Charged \(+2\), stopped by a few centimeters of air or a sheet of paper.
- Beta Particles: Charged \(-1\), travel a few meters in air or millimeters in aluminum.
- Gamma Rays: Uncharged, travel centimeters in lead or long distances through air.
- Neutrinos: Can travel through miles of lead without interaction.
- In living organisms, radiation causes its damage mainly by ionization in the living cells.
- All three particles energize atoms in living tissue to the point that they lose electrons and become ionized.
Background radiation
Background radiation is the ionizing radiation that people are exposed to in everyday life, including natural and artificial sources.
Radioactive decay
Stable isotopes exist for elements having atomic numbers Z = 1 to 83.
Up to Z = 20, the neutron-to- proton ratio is close to 1.
Beyond Z = 20, the neutron-to- proton ratio is bigger than 1, and grows with atomic number.
The extra neutrons counteract the repulsive Coulomb force between protons by increasing the strong force but not contributing to the Coulomb force.
Half-life
- As we have seen, some nuclides are unstable.
- What this means is that an unstable nucleus may spontaneously decay into another nucleus (which may or may not be stable).
- Given many identical unstable nuclides, which precise ones will decay in any particular time is impossible to predict.
- In other words, the decay process is random.
- But random though the process is, if there is a large enough population of an unstable nuclide, the probability that a certain proportion will decay in a certain time is well defined.
EXAMPLE: Here we have a collection of unstable Americium-241 nuclides.
We do not know which particular nucleus will decay next.
All we can say is that a certain proportion will decay in a certain amount of time.
- Obviously the higher the population of Americium-241 there is to begin with, the more decays there will be in a time interval.
- But each decay decreases the remaining population.
- Hence the decay rate decreases over time for a fixed sample.
- It is an exponential decrease in decay rate.
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- Thus the previous graph had the time axis in increments of half-life.
- From the graph we see that half of the original 100 nuclei have decayed after 1 half-life.
- Thus after 1 half-life, only 50 of the original population of 100 have retained their original form.
- And the process continues
- Rather than measuring the amount of remaining radioactive nuclide there is in a sample (which is extremely hard to do) we measure instead the decay rate (which is much easier).
- Decay rates are measured using various devices, most commonly the Geiger-Mueller counter.
- Decay rates are measured in Becquerels (Bq).
Solving problems involving integral numbers of half-lives
- The decay rate or activity A is proportional to the population of the radioactive nuclide N0 in the sample.
- Thus if the population has decreased to half its original number, the activity will be halved.
Example
A radioactive sample’s activity decreases from \(X \, \text{Bq}\) to \(\frac{X}{16} \, \text{Bq}\) in 80 minutes.
▶️Answer/Explanation
Solution:
\(N_0 \rightarrow \frac{1}{2}N_0 \rightarrow \frac{1}{4}N_0 \rightarrow \frac{1}{8}N_0 \rightarrow \frac{1}{16}N_0\)
Four half-lives = 80 minutes.
Half-life \(t_{\text{half}} = 20 \, \text{minutes}\).
IB Physics Radioactivity Exam Style Worked Out Questions
Question
When alpha particle scattering experiments were carried out with high-energy alpha particles, deviations from Rutherford scattering were observed. What was deduced as a result of this observation?
A. The size of the alpha particle
B. The size of the nucleus
C. The nature of the electrostatic field inside the nucleus
D. The nature of the weak nuclear force within the nucleus
▶️Answer/Explanation
Ans B
Question
Radioactive nuclide $\mathrm{X}$ decays into a stable nuclide $\mathrm{Y}$. The decay constant of $\mathrm{X}$ is $\lambda$. The variation with time $t$ of number of nuclei of $X$ and $Y$ are shown on the same axes.
What is the expression for $s$ ?
A. $\frac{\ln 2}{\lambda}$
B. $\frac{1}{\lambda}$
C. $\frac{\lambda}{\ln 2}$
D. $\ln 2$
▶️Answer/Explanation
Ans:A