Radioactive Decay (HL IB Physics)

Two samples P and Q of different radioactive isotopes have the same initial activity. Sample P has a third of the number of atoms as sample Q. The half-life of P is T seconds.

What is the half-life of sample Q?

The half-life of a radioactive isotope is 10 days. What is the approximate percentage of the sample remaining after 25 days?

A pure sample of a radioactive nuclide undergoes a decay resulting in a stable daughter nuclide. What fraction of the sample is made up of the daughter nuclide after five half-lives?

 decays to thorium-234 by emitting an alpha particle and two gamma rays. Thorium-234 then decays into protactinium via beta decay.

Which point on the N-Z graph below represents the position of the granddaughter nucleus, protactinium?

The half-life of carbon-14 is 6000 years.

An ancient elephant tusk has been uncovered and its age is unknown. A 20 g sample of the tusk has an activity of 1.25 Bq due to carbon-14.

A 80 g sample of tusk taken from a living elephant has an activity of 20 Bq.

Use this information to determine the age of the ancient tusk.

Fluorodeoxyglucose is a compound used as a tracer in medical imaging. The isotope fluorine-18 is used, which is a positron emitter.

The way these positrons interact with electrons in the body allows PET (positron emission tomography) scanners to determine the rate of respiration certain cells are performing.

Fluorine-18 decays into an isotope of oxygen.

Which equation below represents the correct nuclear equation for this decay?

Protactinium-231 () is a radioactive element, it decays by alpha radiation and then beta-minus decay as shown below:

What proton number and mass number will element B have?

A radioactive source is known to emit  radiation. A Geiger-Muller tube is used to measure the count rate at increasing distances from the source.

Wh_ich graph correctly represents the variation in count rate over these distances for  radiation?

Unstable nuclei make up 10% of a sample’s mass. The count rate of the sample is measured over a time period of 8 hours.

After some time has passed, the percentage of the sample which is unstable reduces to 2.5%. What is the count rate of the source at this time?

A source is known to be radioactive but the type of radiation being emitted is unknown.

A Geiger-Müller tube is placed close to the source and different materials are placed between the two. A table of the count rates recorded for each material is shown below. The background count rate is 15 counts per minute.

What types of radiation are being emitted by the source?

Three of the four isotopes below are the same element. Which isotope represents a different element?

The image below shows a simplified version of the binding energy per nucleon E of nuclei versus the nucleon number N. Which of the following positions represents nuclei that are the most stable?

The rest-mass of a nucleus of boron-11 is m_B. The rest-masses of a neutron and proton are m_N and m_P respectively.

Which of the following shows the correct calculation for the binding energy of boron-11?

The binding energy per nucleon is 7.98 MeV for an atom of . Approximately how much energy would be needed to completely separate the nucleons of this atom?

The mass defect of a helium-4 nucleus is 5.04 × 10^–29 kg.

What is the binding energy of a helium-4 nucleus?

Two identical nuclei of mass m fuse to form a single heavier nucleus (with no other products) with mass M. Which of the following statements is correct?

Nitrogen-14 can be transformed into Oxygen-17 by bombardment with high energy alpha particles, as described in the nuclear reaction equation below:

The total rest mass of the reactants is 18.006 u and total rest mass of the products is 18.007 u.

Which of the following statements about this reaction is correct?

The graph below shows how the average binding energy per nucleon varies with nucleon number for stable nuclei.

Approximately how much energy is released when the nucleus  forms?

Which statement about nuclear binding energy is correct?

A series of radioactive decays produce both alpha particles and anti-electron neutrinos.

Which row describes the nature of the energy spectrum of these two particles?

The decay of several unstable nuclei are observed in a radiation chamber. The following identifications are made: 

1. Alpha-particles have discrete kinetic energy levels
2. Beta-particles have a continuous range of kinetic energies
3. Gamma-ray photons have discrete kinetic energy levels

These observations directly relate to two important discoveries; the use of emission spectra to identify elements and the existence of the neutrino.

Which row correctly identifies the observations that lead researchers to the discovery of emission spectra and the existence of the neutrino?

A radioactive sample of initial activity 10.0 Bq has a half-life of 1 day.

What is the activity of the sample after 2.5 days?

A radioactive source X consists of 10.4 × 10¹¹ atoms of a nuclide of half-life 5 days. A second source Y consists of 5.2 × 10¹⁰ atoms of another nuclide of half-life 6 days.

After how many days will the number of radioactive atoms in X be equal to Y?

Two radioactive elements X and Y have half–lives T_X and T_Y respectively. Initially samples of S, N_X contains three times as many atoms of Y, N_Y .

After a certain time t, which of the expressions for  is correct?

A pure sample of a radioactive nuclide of mass m has a half-life of T_1/2 and an initial activity of A₀.

What is the half-life and initial activity of a pure sample of the same radioactive nuclide of mass 3m?

	Half-life	Initial activity
A.
B.
C.
D.

Two radioactive nuclides, P and Q, have half-lives of 70 s and 175 s respectively. At time t = 0, samples of P and Q contain the same number of nuclei.

What is when t = 350 s?

Two unstable isotopes are initially present in equal numbers. Isotope Y has a half-life of 6 minutes and isotope Z has a half-life of 3 minutes.

Which expression correctly describes the ratio of the activity of Y to Z after 12 minutes?

A pure sample of a known element has a very short half-life. What measurement(s), together with the initial activity of the sample, must be made in order to measure the half-life of the element?

A particular nucleus, decays to form , which then has two possible decay paths, resulting in either an isotope of Thallium (Tl) or Polonium (Po), as shown.

Which isotope could not be ?

The decay series for Thorium–232 can be plotted as shown.

According to the diagram, how many possible routes are available for Thorium–232 to decay to a stable nucleus of lead−208?

The diagram shows the decay chain for a particular isotope.

What are the isotopes labelled 1, 2 and 3?

	1	2	3
A
B
C
D

Polythene film is made by extruding polythene and drawing it into a long sheet which is wound onto a roll, as shown in the diagram below.

The manufacturer has to carefully choose a radioactive isotope which will effectively remove any electrostatic charge that has built up on the film. The manufacturer also has to consider the point X, Y or Z at which the radioactive isotope should be placed along the assembly line.

At which point should the radioactive isotope be placed, and which type of radiation should the manufacturer choose to remove excess electrostatic charge?

Radioactive isotopes are used in medical imaging.

Two isotopes of iodine,  and , are used by radiographers to give to patients in the form of iodide before taking scans.

The incomplete decay equations for these isotopes are:

Which statement gives the correct difference between these two decays?

The graph shows the how the neutron-proton ratio of stable nuclei changes as proton number increases.

What other changes with increasing proton number are suggested by the graph?

1. The charge-mass ratio increases
2. The charge-mass ratio decreases
3. The likelihood of α-decay increases
4. The likelihood of β-positive decay increases
5. Protons outnumber neutrons in large nuclei, with a rapidly increasing ratio

The charge to mass ratio, , is also known as the specific charge.

What is the ratio of ?

The number of undecayed atoms, N, of a radioactive substance after time, t, can be calculated by the equation:

Where:

• = the half-life 
• = the original number of atoms

Two radioactive elements X and Y have half–lives T_X and T_Y respectively. An initial sample contains three times as many atoms of X, N_X than atoms of Y, N_Y.

After a certain time, t, which of the expressions for is correct?

A nucleus has a mass M. 

Which of the following expressions correctly represents the binding energy per nucleon of this nucleus in terms of the speed of light c, the mass of a proton m_p and the mass of a neutron m_n? 

A nuclear reaction can be written in the form:

Energy is released during this reaction. 

Which of the following is correct regarding the masses m and the binding energies b of the nuclides?

	Binding energy	Mass
A.
B.
C.
D.

One possible fission reaction for uranium−235 is:

The proton number of barium is 20 more than the proton number of krypton. The measured mass of this nucleus is M.

Which expression gives the mass defect associated with the krypton nucleus?

A stationary uranium-238 nucleus decays by alpha-emission, as shown in the equation below:

This decay generates a total energy E. 

Which of the following statements is correct regarding the kinetic energy of the alpha particle?