Exercises: Radioactivity and nuclear processes

Unstable nuclei emit three types of radiation: alpha ($\alpha$), beta ($\beta$) and gamma ($\gamma$).

1. a) State the nature of each: is it a helium nucleus, an electron or a photon?
2. b) Order them from smallest to largest mass.
3. 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 diagram:

1. a) Match each material with the type of radiation (alpha, beta or gamma) it is sufficient to stop.
2. b) Which of the three types of radiation is the most penetrating? And the least?
3. 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.

1. 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 $Z$.
2. 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 (${}^{0}_{-1}\text{e}$) is emitted.

1. a) Write the equation for the process, ${}^{14}_{6}\text{C} \rightarrow {}^{A}_{Z}\text{N} + {}^{0}_{-1}\text{e}$, calculating $A$ and $Z$.
2. b) Explain why in beta decay the mass number does not change, but the atomic number does.

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.

1. a) How many grams remain undecayed after one half-life has passed?
2. b) And after two half-lives? And three?
3. c) Write down, in terms of $n$, the general expression for the fraction remaining after $n$ half-lives.

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:

1. a) Explain what gamma radiation is: how is it similar to visible light and how is it different?
2. b) Do the mass number $A$ or the atomic number $Z$ of the nucleus change when it emits gamma? Justify your answer.

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).

1. a) In a laboratory sample, $12000$ decays are counted in one minute: calculate its activity in becquerels.
2. b) Explain what happens to the activity of a sample as time passes, relating it to the decrease in the number of nuclei.

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:

1. a) Write the equation for the first decay and identify the daughter nuclide (it is an isotope of radium, with $Z = 88$).
2. b) Write the equation for the second decay and identify the final nuclide (it is an isotope of actinium, with $Z = 89$).
3. c) Verify that mass number and atomic number are conserved in each step.

Alpha radiation is the most ionising of the three and yet the least penetrating; gamma is the most penetrating and the least ionising.

1. a) Explain what it means for radiation to be ionising.
2. b) Reason why alpha radiation, with its high ionising power, barely penetrates the outer layer of skin.
3. 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.

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:

1. 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 $A = 206$.
2. 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 $Z = 82$.
3. c) Verify that the final balance of the two conservation laws is consistent.