Decay constant and exponential decay

Explain what is meant by a tracer.

A technetium‑99m tracer with an activity of 900 MBq is injected into a body. The half‑life of technetium‑99m is 6.01 hours.

Calculate the number of technetium‑99m nuclei initially present in the tracer.

Calculate the time in hours taken for the activity of the tracer to have fallen to 3.0% of its initial activity.

A researcher is doing an experiment on a radioactive solution in a thin glass tube. The solution has two radioactive materials X and Y. The table below shows some data on these two materials.

The solution has the same number of nuclei of X and Y at the start.

State and explain which material has the greatest activity at the start.

State why it is dangerous for the researcher to handle the test tube with bare hands.

Carbon-14 (¹⁴₆C) is produced in the upper atmosphere of the Earth by collisions between nitrogen nuclei and fast-moving neutrons. The nuclear transformation equation below shows the formation of a single carbon-14 nucleus.

State the proton number of particle X.

Use the data below to determine the binding energy per nucleon of the¹⁴₆C nucleus. Write your answer to 3 significant figures.

• mass of neutron = 1.675 × 10^–27 kg

• mass of proton = 1.673 × 10^–27 kg

• mass of¹⁴₆C nucleus = 14.000 u

• 1 u = 1.66 × 10^–27 kg

binding energy per nucleon =........ J per nucleon

A student is modelling the decay of a radioactive source using the equation N / t = −0.5 N. The student decides to use t = 0.10 s. The number N of radioactive nuclei is 2000 at t = 0.

Part of the modelling spreadsheet from the student is shown below.

What is the value of N at t = 0.30 s?

A 1700

B 1710

C 1715

D 1805

Your answer

The half-life of the isotope carbon-14 is 5700 years (y).

Carbon-dating is a technique used to date an ancient wooden axe. The ratio of carbon-14 to carbon-12 in the axe material is 78% of the current ratio of carbon-14 to carbon-12 in a living tree.

Calculate the age in years of the wooden axe.

State one assumption made in the calculation in (ii).

Fig. 20 illustrates a device used to determine the relative abundance of charged rubidium ions.

A uniform magnetic field is applied to an evacuated chamber. The direction of the magnetic field is perpendicular to the plane of the paper.

A beam of positive rubidium ions enters the chamber through a hole at H. The ions travel in a semi-circular path in the magnetic field. The ions are detected at point D.

The chemical composition of ancient rocks found on the Earth can be used to estimate the age of the Earth. Nuclei of rubidium-87 (⁸⁷₃₇Rb) decay spontaneously into nuclei of strontium-87 (⁸⁷₃₈Sr). The half-life of rubidium-87 is 49 billion years.

Name the two leptons emitted in the decay of a rubidium-87 nucleus.

The percentage of rubidium left in a sample of an ancient rock is 95%.

Estimate the age of the Earth in billion years.

age =........ billion years

An isotope of polonium-213 (²¹³₈₄Po) first decays into an isotope of lead-209 (²⁰⁹₈₂Pb) and this lead isotope then decays into the stable isotope of bismuth (Bi).

Fig. 24 shows two arrows on a neutron number N against proton number Z chart to illustrate these two decays.

Complete the nuclear decay equations for

the polonium isotope

the lead isotope.

A pure sample of polonium-213 is being produced in a research laboratory. The half-life of²¹³₈₄Po is very small compared with the half-life of²⁰⁹₈₂Pb.

After a very short time, the ionising radiation detected from the sample is mainly from the beta-minus decay of the lead-209 nuclei.

Briefly describe and explain an experiment that can be carried out to confirm the beta-minus radiation emitted from the lead nuclei.

The activity of the sample of²⁰⁹₈₂Pb after 7.0 hours is 12 kBq. The half-life of²⁰⁹₈₂Pb is 3.3 hours.

Calculate the initial number of lead-209 nuclei in this sample.

Fluorine-18 is a common radioactive isotope used in positron emission tomography (PET). Fluorine-18 emits positrons. A patient is injected with a radiopharmaceutical containing fluorine-18.

Describe how a PET scanner is used to locate an area of increased activity within the patient.

The half-life of fluorine-18 is 110 minutes. Calculate the time t in minutes for the activity of the radiopharmaceutical to decrease to 30% of its initial activity.

PET scanners are not available in all hospitals. This is because fluorine-18 requires expensive on-site particle accelerators and fluorine-18 has a very small ‘shelf-life’. Suggest the impact this may have on the treatment and diagnosis of patients in the country.