Relativistic, quantum, nuclear, and particle physics · Nuclear physics
Radioactivity and nuclear processes
The radon that seeps up from the granite under parts of Wicklow, Galway and Donegal comes from uranium that has been decaying, nucleus by nucleus, ever since the Earth formed 4,500 million years ago, and nobody can predict when a particular atom's turn will come. And yet, with a sample of billions of atoms, we can predict with great statistical precision how much will be left in a year, a century or a millennium. That combination of individual chance and statistical certainty is the heart of radioactivity.
The three types of radioactivity: alpha, beta and gamma
When the radiation from uranium is passed through an electric or magnetic field, and through sheets of different materials and thicknesses, it separates into three types by how they are deflected and how far they penetrate: one positive, only slightly deflected and easily absorbed; one negative, strongly deflected and of intermediate penetration; and one neutral, undeflected and extraordinarily penetrating. Which nuclear transformations produce these very different emissions?
Gamma radiation and ionisation
Even with no source nearby, a Geiger-Müller (GM) tube clicks now and then. This is natural background radiation, which comes from radon gas, rocks, cosmic rays and food. It is always present, so it must be measured first and subtracted from any count rate you record in the lab.
Gamma radiation is electromagnetic radiation, like visible light, but each photon carries far more energy. After an alpha or beta decay the daughter nucleus is often left excited; it drops to a lower energy level and emits a gamma photon, so $A$ and $Z$ do not change.
Radiation is ionising if it carries enough energy to knock electrons out of atoms, leaving charged ions. Alpha particles ionise most strongly but lose their energy in a very short distance.
For radiation safety, reduce the time of exposure, increase the distance from the source and use suitable shielding (paper or skin for alpha, aluminium for beta, lead or thick concrete for gamma).
In an electric or magnetic field the three types behave differently: alpha (charge $+2e$, mass about 4 u) is deflected one way, only slightly because it is heavy; beta minus (charge $-e$, tiny mass) is deflected the opposite way, strongly; gamma has no charge and is not deflected. This is why an alpha source such as the americium-241 in a smoke detector is safe behind its casing but dangerous if inhaled or swallowed, where it irradiates living tissue directly.
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Unstable nuclei emit three types of radiation: alpha ($\alpha$), beta ($\beta$) and gamma ($\gamma$). a) State the nature of each: is it a helium nucleus, an electron or…
Unstable nuclei emit three types of radiation: alpha ($\alpha$), beta ($\beta$) and gamma ($\gamma$).
a) State the nature of each: is it a helium nucleus, an electron or a photon?
b) Order them from smallest to largest mass.
c) Indicate which ones have an electric charge and what sign it is.
In a laboratory there are three protective materials: a sheet of paper, an aluminium plate a few millimetres thick, and a thick wall of lead or concrete. Observe the…
In a laboratory there are three protective materials: a sheet of paper, an aluminium plate a few millimetres thick, and a thick wall of lead or concrete. Observe the diagram:
a) Match each material with the type of radiation (alpha, beta or gamma) it is sufficient to stop.
b) Which of the three types of radiation is the most penetrating? And the least?
c) Explain why technicians working with gamma sources use lead shields or aprons.
Uranium-238 decays by emitting an alpha particle (a helium-4 nucleus, ${}^{4}{2}\text{He}$) and transforms into thorium. a) Write the complete equation for the process,…
Uranium-238 decays by emitting an alpha particle (a helium-4 nucleus, ${}^{4}_{2}\text{He}$) and transforms into thorium.
a) Write the complete equation for the process, ${}^{238}_{92}\text{U} \rightarrow {}^{A}_{Z}\text{Th} + {}^{4}_{2}\text{He}$, calculating the values of $A$ and $Z$.
b) State the two conservation laws you have applied: conservation of mass number and conservation of atomic number.
Carbon-14, used in the dating of archaeological remains, decays by beta-minus emission: a neutron in the nucleus converts into a proton and an electron…
Carbon-14, used in the dating of archaeological remains, decays by beta-minus emission: a neutron in the nucleus converts into a proton and an electron (${}^{0}_{-1}\text{e}$) is emitted.
a) Write the equation for the process, ${}^{14}_{6}\text{C} \rightarrow {}^{A}_{Z}\text{N} + {}^{0}_{-1}\text{e}$, calculating $A$ and $Z$.
b) Explain why in beta decay the mass number does not change, but the atomic number does.
After many alpha or beta decays, the daughter nucleus is left in an excited state and de-excites by emitting gamma radiation. Observe the energy level diagram: a)…
After many alpha or beta decays, the daughter nucleus is left in an excited state and de-excites by emitting gamma radiation. Observe the energy level diagram:
a) Explain what gamma radiation is: how is it similar to visible light and how is it different?
b) Do the mass number $A$ or the atomic number $Z$ of the nucleus change when it emits gamma? Justify your answer.
Alpha radiation is the most ionising of the three and yet the least penetrating; gamma is the most penetrating and the least ionising. a) Explain what it means for…
Alpha radiation is the most ionising of the three and yet the least penetrating; gamma is the most penetrating and the least ionising.
a) Explain what it means for radiation to be ionising.
b) Reason why alpha radiation, with its high ionising power, barely penetrates the outer layer of skin.
c) Americium-241 in smoke detectors emits alpha radiation: explain why it poses no danger while it remains inside its casing, but would be dangerous if inhaled or ingested.
Thorium-232 (${}^{232}{90}\text{Th}$) first emits an alpha particle (${}^{4}{2}\text{He}$) and the resulting nucleus then emits a beta-minus particle…
Thorium-232 (${}^{232}_{90}\text{Th}$) first emits an alpha particle (${}^{4}_{2}\text{He}$) and the resulting nucleus then emits a beta-minus particle (${}^{0}_{-1}\text{e}$). Observe the diagram of the decay chain:
a) Write the equation for the first decay and identify the daughter nuclide (it is an isotope of radium, with $Z = 88$).
b) Write the equation for the second decay and identify the final nuclide (it is an isotope of actinium, with $Z = 89$).
c) Verify that mass number and atomic number are conserved in each step.
In the uranium radioactive decay series, the radium-226 nucleus (${}^{226}{88}\text{Ra}$) eventually transforms into lead-206 (${}^{206}{82}\text{Pb}$) by emitting only…
In the uranium radioactive decay series, the radium-226 nucleus (${}^{226}_{88}\text{Ra}$) eventually transforms into lead-206 (${}^{206}_{82}\text{Pb}$) by emitting only alpha and beta-minus particles. Observe the diagram:
a) Each alpha emission reduces $A$ by $4$ units and each beta-minus emission does not change it: calculate how many alpha particles are emitted in total to go from $A = 226$ to $A = 206$.
b) Taking into account that each alpha particle reduces $Z$ by $2$ units and each beta-minus increases it by $1$, calculate how many beta-minus emissions are needed to end at $Z = 82$.
c) Verify that the final balance of the two conservation laws is consistent.
The half-life of a radioactive isotope is the time taken for the amount of undecayed nuclei to halve. A laboratory source contains $100\ \text{g}$ of a certain isotope.…
The half-life of a radioactive isotope is the time taken for the amount of undecayed nuclei to halve. A laboratory source contains $100\ \text{g}$ of a certain isotope. The figure shows its decay curve.
a) How many grams remain undecayed after one half-life has passed?
b) And after two half-lives? And three?
c) Write down, in terms of $n$, the general expression for the fraction remaining after $n$ half-lives.
The activity of a radioactive sample is the number of decays that occur in it per second, and is measured in becquerels ($1\ \text{Bq} = 1$ decay per second). a) In a…
The activity of a radioactive sample is the number of decays that occur in it per second, and is measured in becquerels ($1\ \text{Bq} = 1$ decay per second).
a) In a laboratory sample, $12000$ decays are counted in one minute: calculate its activity in becquerels.
b) Explain what happens to the activity of a sample as time passes, relating it to the decrease in the number of nuclei.
Both when a massive uranium nucleus is split by a neutron and when two tiny hydrogen nuclei are forced together at millions of degrees, the products weigh less than the reactants and release a colossal amount of energy; how can two geometrically opposite processes release energy at both ends of the periodic table?
Balancing nuclear reactions and mass defect
In fission and fusion equations the total $A$ and total $Z$ are the same on both sides, so a missing product or a number of neutrons can be found by balancing. The energy released comes from the mass defect $\Delta m$, the drop in total mass: $E = \Delta m\, c^2$, with $1\ \text{u}\cdot c^2 = 931.5\ \text{MeV}$ and $1\ \text{eV}=1.6\times10^{-19}\ \text{J}$. Fusion needs very high temperatures because the nuclei, both positive, repel each other with the electrostatic force and must get within about $10^{-15}\ \text{m}$, where the strong nuclear force takes over.
Exponential law, activity and dating
Even with no source nearby, a Geiger-Müller (GM) tube clicks now and then: this is natural background radiation, from radon gas, rocks, cosmic rays and food, and it must be subtracted from a count rate. A Geiger counter placed in front of a pure sample of radon-222 records, on average, half as many clicks per minute (after subtracting the background count) every 3.8 days, regardless of temperature, pressure or the chemical bonding of the sample; what mathematical law governs this decreasing rate of decays?
If you are given a mass of radionuclide, first calculate $N=(m/M)N_A$, using consistent units of mass. If it is an impurity, distinguish percentage by mass from percentage of atoms. Dating assumes that the initial proportion is known or can be estimated and that the system has remained closed; carbon-14 requires calibration in real applications.
In $\beta^-$ decay an antineutrino is emitted: $\text n\to\text p+\text e^-+\bar\nu_e$. In $\beta^+$ decay a positron and a neutrino are emitted: $\text p\to\text n+\text e^++\nu_e$ inside a nucleus with an allowed energy balance; $A$ does not change and $Z$ decreases by one. Conservation of charge and energy must accompany the balance of nuclear numbers.
Let's practice! 2 medium exercises in this section
Back to the beginning: Uranium-238 has a half-life of $4.5\times10^9$ years: since the Earth is about that age, about one half-life has elapsed, so roughly $50\%$ of the primordial uranium-238 survives, still decaying slowly into the radon found in some Irish homes.
Summary
Let's practice! 2 medium exercises in this section