Syllabus Edition

First teaching 2023

First exams 2025

|

Radioactive Decay (HL IB Physics)

Topic Questions

5 hours79 questions
1a
Sme Calculator
3 marks

Nuclides can be written in symbol form. 

Complete the labels on the general nuclide symbol using the words below:

7-1-q2a-question-sl-sq-easy-phy
  • Chemical symbol for the element  
  • Proton number
  • Nucleon number
1b
Sme Calculator
4 marks

Define radioactive decay.

1c
Sme Calculator
3 marks

Draw lines to match the phrases with the correct definitions.

7-1-q2c-question-sl-sq-easy-phy
1d
Sme Calculator
1 mark

The graph shows the count rate of a radioactive substance measured by a Geiger-Müller tube.

7-1-q2d-question-sl-sq-easy-phy

State what the fluctuations in the count rate provide evidence for.

Did this page help you?

2a
Sme Calculator
3 marks

The number of neutrons and number of protons for different isotopes can be plotted on a graph called a nuclear stability curve. Different regions on the graph represent the type of decay which is expected.

The three types of radioactive particles shown are alpha emitters, beta−minus emitters and beta−positive emitters.

Label the regions of the graph to indicate which type of radioactive particle is expected to be emitted.

7-1-q3a-question-sl-sq-easy-phy
2b
Sme Calculator
8 marks

Background radiation comes from a variety of sources, some are natural and some are man-made.

Place ticks (✔) in the correct column to indicate whether the source is man-made or natural:

7-1-q3b-question-sl-sq-easy-phy
2c
Sme Calculator
4 marks

Radiation is emitted as various different types of particle. 

State 4 types of radioactive particle.

2d
Sme Calculator
4 marks

When a beta emission occurs, a particle called a neutrino is also emitted.

Complete the gaps in the following sentences. Choose from the words below:

A neutrino has no ___________ and negligable __________. Electron anti−neutrinos are produced during ___________ decay. Electron neutrinos are produced during ___________ decay. 

 

 mass     gravity     age     charge     beta−minus     beta−positive      alpha   

Did this page help you?

3a
Sme Calculator
6 marks

Complete the table with the correct properties of alpha, beta−minus, beta−positive and gamma radiation.

7-1-q4a-question-sl-sq-easy-phy
3b
Sme Calculator
2 marks

Plutonium−239 decays to Uranium−235 through the emission of an alpha particle.

Determine the missing values in the decay equation:

 
Pu presubscript 94 space end presubscript presuperscript 239 space end presuperscript rightwards arrow straight U presubscript 92 space end presubscript presuperscript left parenthesis straight i right parenthesis space end presuperscript plus straight alpha presubscript left parenthesis ii right parenthesis end presubscript presuperscript 4 space end presuperscript

 

3c
Sme Calculator
2 marks

Strontium−90 decays through beta−minus decay to form Yttrium−90.

Determine the missing values in the decay equation.

 

Sr presubscript 38 space end presubscript presuperscript 90 space end presuperscript rightwards arrow straight Y presubscript left parenthesis straight i right parenthesis end presubscript presuperscript 90 plus beta presubscript negative 1 space end presubscript presuperscript 0 space end presuperscript plus left parenthesis ii right parenthesis

3d
Sme Calculator
2 marks

Fluorine−18 decays through beta−plus decay to form oxygen−18.

Determine the missing values in the decay equation.

 

straight F presubscript 9 space end presubscript presuperscript 18 space end presuperscript rightwards arrow straight O presubscript 8 presuperscript left parenthesis straight i right parenthesis end presuperscript plus beta presubscript left parenthesis ii right parenthesis space end presubscript presuperscript 0 space end presuperscript plus nu subscript e

Did this page help you?

4a
Sme Calculator
2 marks

Define: 

(i)
Binding energy.
[1]
(ii)
Mass defect.
[1]
4b
Sme Calculator
4 marks

The nuclear rest mass of oxygen−16 open parentheses O presubscript 8 presuperscript 16 close parentheses is 15.994 914 u. 

The mass defect, Δm, equation describes the relationship between the proton number, Z, the number of neutrons, N, the proton rest mass, mp, the neutron rest mass, mn, and the nuclear rest mass, mtotal.

straight capital delta m equals Z m subscript p space plus space N m subscript n minus m subscript t o t a l end subscript

Calculate the mass defect of oxygen−16. Give your answer to 6 d.p.

4c
Sme Calculator
3 marks

The mass defect (from part (b)) can be used to calculate the binding energy.

Calculate the total binding energy for a nucleus of oxygen−16 in J

4d
Sme Calculator
2 marks

Determine the binding energy per nucleon of oxygen−16 in J.

Did this page help you?

5a
Sme Calculator
3 marks

The chart shows the binding energy per nucleon for a number of nuclei.

7-2-q4a-question-sl-sq-easy-phy

Label the chart to show: 

(i)
Where fusion of these elements occurs to release energy
[1]
(ii)
Where fission of these elements occurs to release energy
[1]
(iii)
The location of Iron open parentheses Fe presubscript 26 presuperscript 56 close parentheses by drawing an X
[1]
5b
Sme Calculator
4 marks

In terms of the forces acting within the nucleus, explain why: 

(i)
Fusion occurs for nuclides with low nucleon numbers.
[2]
(ii)
Fission occurs for nuclides with high nucleon numbers.
[2]
5c
Sme Calculator
4 marks

In both fission and fusion, there is a mass defect between the original nuclei and the daughter nuclei.

Complete the sentences by circling the correct word. 

In fusion, the mass of the nucleus that is created is slightly more / less than the total mass of the original nuclei and the daughter nucleus is more / less stable.  

In fission, an unstable nucleus is converted into more stable nuclei with a larger / smaller total mass. In both cases, this difference in mass, the mass defect, is equal to the binding energy that is released. 

Fission / Fusion releases much more energy per kg than fission / fusion. The greater the increase in binding energy, the more / less energy is released.

5d
Sme Calculator
3 marks

The graph shows the binding energy per nucleon in MeV plotted against nucleon number, A.

7-2-q4d-question-sl-sq-easy-phy

Use the graph to find the binding energy of the following nuclei. 

(i)
Platinum−190.
[1]
(ii)
Silicon−28.
[1]
(iii)
Tellurium−120.
[1]

Did this page help you?

6a
Sme Calculator
3 marks

The graph below shows the binding energy per nucleon against the number of nucleons in the nucleus.

7-2-q5a-question-sl-sq-easy-phy

There are three nuclei, labelled X, Y and Z, which do not sit on the line of the graph.

Match up the labels to the correct element by drawing a line between the boxes

 
7-2
6b
Sme Calculator
3 marks

Helium can fuse together to form beryllium as shown in the reaction below:

7-2-q5b-question-sl-sq-easy-phy

State and explain which is larger, the mass of the reactants or the mass of the products.

6c
Sme Calculator
5 marks

The table shows the mass of each reactant and daughter nucleus:

7-2-c

Using the information in the table:

 
(i)
Calculate the mass of the reactants, mR in atomic mass units.
[2]
(ii)
Calculate the mass defect, Δm, between the reactants and the daughter nuclei in atomic mass units.
[3]
6d
Sme Calculator
2 marks

Helium−3 and helium−4 fuse together to form beryllium−7.

The mass defect, Δm for this fusion reaction is equal to 2.8 × 10–30 kg. 

Calculate the energy released, ΔE, in the fusion of beryllium7.

Did this page help you?

7a
Sme Calculator
2 marks

Outline what is meant by the term decay constant.

7b
Sme Calculator
5 marks

A sample of 2.5 mol of the radioactive nuclide plutonium-239 decays into uranium-235 with the production of another particle.

P presubscript 94 presuperscript 239 u space rightwards arrow space straight U presubscript 92 presuperscript 235 space plus space straight X

(i)
Identify particle X.
[1]
(ii)
The radioactive decay constant of plutonium-239 is 9.5 × 10−13 s−1. Determine the time required to produce 1 mol of uranium-235.

[4]

7c
Sme Calculator
5 marks

Thorium-227 is one of the isotopes formed after a uranium-235 nucleus has undergone a series of decays.

One sample of thorium-227 has a decay constant of 0.037 day−1 and an initial activity of 46 Bq. 

 
(i)
State what is meant by the activity of a sample.
[2]
(ii)
Calculate the activity of the sample after one week.
[3]

Did this page help you?

8a
Sme Calculator
5 marks

The isotope bismuth-212 undergoes α-decay to an isotope of thallium-208. In this decay, a gamma-ray photon is also produced.

bismuth-212-levels

(i)
Complete the nuclear energy level diagram to indicate the alpha decay of Bi-212 into Tl-208, followed by the emission of a photon of energy 0.493 MeV.
[2]
 
(ii)
Outline how the alpha particle spectrum and the gamma spectrum of the decay of bismuth-212 give evidence for the existence of discrete nuclear energy levels, by completing the following sentences:

The emitted alpha particles have ......................... energies.

The emitted gamma rays have ......................... energies.

Therefore, nuclear energy levels must be discrete because the energies of the alpha particles and the gamma photons are determined by ........................................................................... .

[3]

8b
Sme Calculator
5 marks

 The isotope potassium-40 can decay via different decay modes to form isotopes of argon-40 or calcium-40.

potassium-energy-levels-qs

(i)
Complete the nuclear energy level diagram to indicate the different modes of decay.

[3]

(ii)
Outline how the β spectrum of the decay of potassium-40 led to the existence of the neutrino being postulated, by completing the following sentences:

The total energy released in any beta decay is ........................., however, the majority of beta particles are found to have energies ......................... than this value.

The distribution of energy values for the beta particles is not ........................., it is found to be a ......................... spectrum.

The existence of the neutrino was postulated to account for the ..........................

The total energy of the decay process must be divided between the ......................... and ......................... .

[2]

8c
Sme Calculator
4 marks

The isotope potassium-40 occurs naturally in many rock formations. The composition of a particular rock sample is found to be 33% potassium-40 atoms out of the total number of argon and potassium-40 atoms.

The half-life of potassium-40 is 1.3 × 109 years.

Determine the age of the rock sample. 

8d
Sme Calculator
6 marks

Bismuth-212 is a short-lived isotope with a half-life of 1 hour.

Briefly outline experimental methods which can measure the half-life of:

 
(i)
Bismuth-212
[3]
(ii)
Potassium-40
[3]

Did this page help you?

1a
Sme Calculator
3 marks

The decay series of an isotope of thorium open parentheses Th presubscript 90 presuperscript 232 close parentheses produces an isotope of radium open parentheses Ra presubscript 88 presuperscript 224 close parentheses. This process involves four separate decays.

The first decay involves the emission of an alpha particle.

Write the decay equation for this process, including the symbol of the daughter product.

1b
Sme Calculator
3 marks

The first decay can be represented on an N-Z diagram as an arrow from point A to point B.

q2b_discrete-energy--radioactivity_ib-sl-physics-sq-medium

Three more decays occur before R presubscript 88 presuperscript 224 a is produced, denoted by “C” on the N-Z diagram.

Outline the possible sequence of decays which lead from point B to C.

1c
Sme Calculator
4 marks

Nuclei can be unstable for a number of reasons.

In terms of forces within the nucleus, explain why large nuclei emit alpha radiation.

1d
Sme Calculator
3 marks

R presubscript 88 presuperscript 224 a then decays four more times, shown below.

q2d_discrete-energy--radioactivity_ib-sl-physics-sq-medium

The first three decays result in the emission of an alpha particle each time. The fourth and final decay results in the emission of a beta-particle.

Calculate the nucleon number and atomic number of nuclide A.

Did this page help you?

2a
Sme Calculator
4 marks

A radioactive source is used to measure the thickness of paper. A Geiger counter is used to measure the count rate on the opposite side of the paper to the radioactive source.  The radioactive source used must be chosen carefully.

(i)
State and explain the type of radioactive source that should be used for this process.  
[2]

(ii)
A new type of paper is placed between the Geiger counter and the radioactive source. Explain how the equipment can be used to show if the new paper is thicker or thinner than the previous type.
[2]
2b
Sme Calculator
2 marks

The arrangement below is used to maintain a constant 0.10 m thickness of aluminium sheets. Alpha, beta or gamma sources are available to be used.

ma3b_discrete-energy--radioactivity_ib-sl-physics-sq-medium

Outline the most suitable radioactive source for this arrangement and explain why the other sources may not be appropriate.

2c
Sme Calculator
3 marks

The source used in part (b) has a half-life of 14 days and it has an initial count rate of 240 counts per minute when first used in the apparatus.

Giving your answer in weeks, calculate the length of time it takes for the Geiger counter to detect a count rate of 0.25 s–1.

2d
Sme Calculator
4 marks

Once the source has reached an activity of 0.25 s–1, it is replaced as the count rate of the source is comparable with that of background radiation.

State two natural sources of background radiation and two man-made sources of background radiation.

Did this page help you?

3a
Sme Calculator
1 mark

A sample’s count rate in counts per minute (cpm) is measured using a  ray detector. This data is plotted on a graph.

q4a_discrete-energy--radioactivity_ib-sl-physics-sq-medium

 

(i)
Use the graph to determine the half-life of this sample.

[2]

(ii)
Explain why the distance between the detector and the source is a control variable.

[2]

3b
Sme Calculator
3 marks

The scientist wonders how the experiment in part (a) would have changed if the sample was twice the size.

Assuming the experiment from part (a) was repeated with a sample the exact same age but twice the mass, calculate the length of time it would have taken to reach a count rate of 22.5 cpm.

3c
Sme Calculator
4 marks

In reality the detector will measure a count rate of more than 5 cpm long after the length of time in part (b) has passed.

(i)
Outline the reason for this larger-than-expected count rate.

[2]

(ii)
Describe the measurements the scientist could take to accurately account for this additional count rate in the final data.

[2]

3d
Sme Calculator
2 marks

The scientist can measure the count rate of the source but is unable to directly measure the activity of the source using their detector. Activity is the total number of particles emitted from the sample per unit time.

Explain why this is not possible.

Did this page help you?

4a
Sme Calculator
4 marks

An unstable isotope of mercury, Hg-203, is tested for its radioactive emissions in a laboratory that has a background rate of 0.3 s–1.

A source is placed a fixed distance from a Geiger-Muller tube. Various materials are placed in between the detector and the source while the count rate is recorded. The results are shown below.

Material

Count rate / s–1

None

68

0.5 mm thick paper

69

2.0 mm thick paper

65

5 cm thick aluminium foil

15

State and explain what types of radiation are being emitted by the Hg-203 source.

4b
Sme Calculator
3 marks

A student notices that the count rate recorded actually increases when 0.5 mm thick paper was placed between the Geiger-Muller tube and the source.

(i)
Suggest one cause of this increase.
[1]

(ii)
Describe what the experimenter could do to check if this data point was anomalous.
[2]

Did this page help you?

5a
Sme Calculator
3 marks

The diagram below shows a plot of binding energy per nucleon against with nucleon number. 

q3a-7-2-sq-medium-ib-physics

Fission and fusion are two nuclear processes in which energy can be released. 

(i)
On the diagram, mark the element with the highest binding energy per nucleon. 

[1]

(ii)
Explain why nuclei that undergo fission are restricted to a different part of the graph than those that undergo fusion.
[2]
5b
Sme Calculator
3 marks

Explain with reference to the figure in part (a), why the energy released per nucleon from fusion is greater than that from fission.

5c
Sme Calculator
2 marks

Explain how the binding energy of an oxygen O presubscript 8 presuperscript 16 nucleus can be calculated with information obtained in the figure from part (a).

5d
Sme Calculator
3 marks

The mass of an O presubscript 8 presuperscript 16 nucleus is 15.991 u. 

Calculate: 

(i)
The mass difference, in kg, of the O presubscript 8 presuperscript 16 nucleus.

 [2] 

(ii)
The binding energy, in MeV, of an oxygen O presubscript 8 presuperscript 16nucleus.

[1]

Did this page help you?

6a
Sme Calculator
3 marks

Bismuth-214 (B presubscript 83 presuperscript 214 i) decays into Polonium-214 (P presubscript 84 presuperscript 214 o) by beta minus decay. 

The binding energy per nucleon of Bismuth-214 is 7.774 MeV and the binding energy per nucleon of Polonium-214 is 7.785 MeV.

Beta-minus decay is described by the following equation:

                                                B presubscript 83 presuperscript 214 i rightwards arrow P presubscript 84 presuperscript 214 o plus beta to the power of minus plus stack v subscript e with bar on top

Show that the energy released in the beta to the power of minus decay of bismuth is about 2.35 MeV and state where the energy comes from.

6b
Sme Calculator
5 marks

If an additional neutron is accelerated into the Polonium-214 (P presubscript 84 presuperscript 214 o) to produce the isotope Polonium-215 (P presubscript 84 presuperscript 215 o), use the following information to deduce the binding energy per nucleon of this new isotope.

 

         Mass of  P presubscript 84 presuperscript 215 o nucleus = 3.571140 × 10−25 kg

6c
Sme Calculator
3 marks

Polonium-215 (P presubscript 84 presuperscript 215 o) is radioactive and decays by the producing alpha radiation, which is known to be a particularly stable. 

Determine the binding energy of alpha radiation. 

The following information is available:

  • Mass of a Helium-4 nucleus: 4.001265 u
6d
Sme Calculator
2 marks

A student claims that the amount of matter within a marble directly converted into energy would be enough to provide 1 year of current human energy consumption globally which is estimated to be 5.80 × 1018 J.

 If the matter within marble is approximately 6.02 × 1023 u, determine if this statement is true, using the mass-energy equivalence.

Did this page help you?

7a
Sme Calculator
2 marks

Explain why the mass of an alpha-particle (α) is less than the total mass of two individual protons and two individual neutrons.

7b
Sme Calculator
2 marks

Show that the energy equivalence of 1.0 u is 931.5 MeV.

7c
Sme Calculator
2 marks

Data for the masses of some nuclei are given below 

Nuclei

Mass / u

Deuterium (H presubscript 1 presuperscript 2)

2.0141

Zirconium (Z presubscript 40 presuperscript 97 r)

97.0980

 

Use the data to determine the binding energy of deuterium in MeV.

7d
Sme Calculator
3 marks

Using the data given in part (c), determine the binding energy per nucleon of zirconium in MeV.

Did this page help you?

8a
Sme Calculator
2 marks

Iodine-131 open parentheses I presubscript 53 presuperscript 131 close parentheses has a half-life of 8.02 days.

Calculate the decay constant of I presubscript 53 presuperscript 131.

8b
Sme Calculator
2 marks

The initial activity of the sample of Iodine−131 is 6.5 × 104 Bq.

Determine the activity after 16 days.

8c
Sme Calculator
2 marks

Determine the mass of the iodine−131 in the sample after 16 days.

8d
Sme Calculator
2 marks

Iodine−131 decays through a number of decay modes. Two of these are straight beta to the power of minus decay of 606 keV and gamma emission of 364 keV. The product of the straight beta to the power of minus decay is Xe presubscript 54 presuperscript 131

Sketch a nuclear energy level diagram to represent these decays. 

Did this page help you?

9a
Sme Calculator
2 marks

A nucleus of sodium−24 decays into a stable nucleus of magnesium−24. It decays by β emission followed by the emission of γ-radiation as the magnesium−24 nucleus de-excites into its ground state.

The sodium−24 nucleus can decay to one of three excited states of the magnesium−24 nucleus. This is shown in the diagram below:

12-2-hl-sqs-medium-q4a-question

The energies of the excited states are shown relative to the ground state.

Calculate the maximum possible speed of the emitted beta particle in MeV.

9b
Sme Calculator
3 marks

The excited magnesium nucleus de-excites through production of gamma radiation of discrete wavelengths.

Calculate the shortest wavelength of emitted radiation.

9c
Sme Calculator
2 marks

The graph shows the activity of a sample of sodium−24 with time.

12-2-hl-sqs-medium-q4c-question

Use the graph to calculate the decay constant of sodium−24.

9d
Sme Calculator
3 marks

The detector in this experiment measures 4% of the activity from the sample.

Determine the activity of sample after 27 hours from the start of the recording,

Did this page help you?

10a
Sme Calculator
2 marks

Americium-241 has a half-life of 432 years. A small sample is held in a school for use in experiments.

The teacher uses a Geiger-Müller counter to measure the count rate at close range. The relationship between activity and count rate is a ratio of 6:1. Over 5 minutes, the count is 13 600. 

Determine the activity of the sample.

10b
Sme Calculator
2 marks

Determine the activity of the americium sample after 748 years.

Did this page help you?

1a
Sme Calculator
2 marks

A radioactive nucleus X presubscript 85 presuperscript 229 undergoes a beta−minus decay followed by an alpha decay to form a daughter nucleus Y presubscript Z presuperscript A.

Write a decay equation for this interaction and hence determine the values of A and Z.

1b
Sme Calculator
3 marks

Thorium open parentheses Th presubscript 90 presuperscript 232 close parentheses decays to an isotope of Radium open parentheses Ra close parentheses through a series of transformations.

The particles emitted in successive transformations are:

alpha space space beta to the power of minus space space beta to the power of minus space space gamma space space alpha

Determine the resulting nuclide after these successive transformations.

Clearly show how you arrive at your final answer.

1c
Sme Calculator
3 marks

Through a combination of successive alpha and beta decays, the isotope of any original nucleus can be formed.

Determine the simplest sequence of alpha and beta decays required to do this and explain your reasoning.

1d
Sme Calculator
2 marks

A nucleus of bohrium open parentheses Bh presubscript straight Y presuperscript straight X close parentheses decays to mendelevium open parentheses Md presubscript 101 presuperscript 255 close parentheses by a sequence of three alpha particle emissions.

Determine the number of neutrons in a nucleus of bohrium.

Did this page help you?

2a
Sme Calculator
3 marks

The table shows some of the isotopes of phosphorus and, where they are unstable, the type of decay.

Isotope P presubscript 15 presuperscript 29 straight P presubscript 15 presuperscript 30 straight P presubscript 15 presuperscript 31 straight P presubscript 15 presuperscript 32 straight P presubscript 15 presuperscript 33
Type of decay beta to the power of plus beta to the power of plus stable   beta to the power of minus


State whether the isotope
P presubscript 15 presuperscript 32 is stable or not. If not, determine, with a reason, the type of decay it experiences.

2b
Sme Calculator
4 marks

The isotope of phosphorus open parentheses straight P presubscript 15 presuperscript 30 close parentheses decays into an isotope of silicon open parentheses Si presubscript Z presuperscript A close parentheses.

(i)
Determine the values of A and Z and write a decay equation for this process.
[2]
(ii)
Explain why each emission product occurs.
[2]

Did this page help you?

3a
Sme Calculator
2 marks

The radioactive isotope uranium−238 decays in a decay series to the stable lead−206. 

The half−life of U presubscript 92 presuperscript 238 is 4.5 × 109 years, which is much larger than all the other half−lives of the decays in the series.

A rock sample, when formed originally, contained 6.0 × 1022 atoms of U presubscript 92 presuperscript 238 and no Pb presubscript 82 presuperscript 206 atoms. At any given time, most of the atoms are either straight U presubscript 92 presuperscript 238 or Pb presubscript 82 presuperscript 206 with a negligible number of atoms in other forms in the decay series.

Sketch on the axes below the variation of number of U presubscript 92 presuperscript 238 atoms and the number of Pb presubscript 82 presuperscript 206 atoms in the rock sample as they vary over a period of 1.0 × 1010 years from its formation. Label your graphs U and Pb.

7-1-ib-sl-hard-sqs-q4a-question

3b
Sme Calculator
2 marks

A certain time, t, after its formation, the sample contained twice as many U presubscript 92 presuperscript 238 atoms as Pb presubscript 82 presuperscript 206 atoms. 

Show that the number of straight U presubscript 92 presuperscript 238 atoms in the rock sample at time t was 4.0 × 1022.

3c
Sme Calculator
2 marks

The ratio of the number of lead nuclei N subscript P b end subscript to the number of uranium nuclei N subscript U at some time t is given by: 

N subscript P b end subscript over N subscript U equals e to the power of lambda t end exponent minus 1

λ is the decay constant and has a value of 1.54 × 10−10 years.

Calculate the time taken (in years) for there to be twice as many straight U presubscript 92 presuperscript 238 atoms as Pb presubscript 82 presuperscript 206 atoms.

3d
Sme Calculator
4 marks

Lead−214 is an unstable isotope of lead−206. It decays by emitting a beta to the power of minus particle to form bismuth−214 (Bi) 

Bismuth is also unstable and has two decay modes: 

  • Emitting an α particle to form thallium−210 (Tl) + energy
  • Emitting a β particle to form polonium−214 (Po) + energy

Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214. Comment on the nature of the energy released. 

Did this page help you?

4a
Sme Calculator
4 marks

Xenon−140 Xe presubscript 54 presuperscript 140 is one of the waste products from the fission of uranium-235. Xenon−140 is radioactive and decays through beta to the power of minus decay.

Xe presubscript 54 presuperscript 140 yields Z space plus space beta to the power of minus sign plus stack nu subscript e with bar on top

The graph shows the variation with time of the mass of 1kg of xenon−140 remaining in the sample.

7-2-ib-sl-hard-sqs-q5c-question

 
(i)
Calculate the proton and mass numbers of nuclide Z.
[1]
(ii)
Calculate the mass of xenon−140 remaining in the sample after 2.5 minutes
[3]
4b
Sme Calculator
4 marks

An alternative nuclear fuel to the traditionally used uranium-235 is thorium-232. When thorium-232 is exposed to neutrons, it will undergo a series of nuclear reactions until it eventually emerges as an isotope of uranium-233, which will readily split and release energy the next time it absorbs a neutron.

Part of the thorium fuel cycle is shown below.

Th presubscript 90 presuperscript 232 space plus space straight n presubscript 0 presuperscript 1 space rightwards arrow space Th presubscript 90 presuperscript 233 space rightwards arrow space Pa presubscript 91 presuperscript 233 space rightwards arrow space straight U presubscript 92 presuperscript 233

Once the uranium-233 nucleus absorbs a neutron, it undergoes fission, releasing energy and two neutrons and forming the fission products Xenon and Strontium as in parts a-c. Any isotopes of uranium-233 which do not undergo fission decay through a chain ending with a stable nucleus of thallium-205 open parentheses Tl presubscript 81 presuperscript 205 close parentheses

Show that 12 particles, not including neutrons, are emitted during this combination of decay chains. Explain your reasoning.

Did this page help you?

5a
Sme Calculator
3 marks

Show that the decay constant is related to the half-life by the expression 

lambda T subscript bevelled 1 half end subscript equals space ln space 2

5b
Sme Calculator
3 marks

Uranium-238 has a half-life of 4.47 × 109 years and decays to thorium-234. The thorium decays (by a series of further nuclear processes with short half-lives) to lead.

Assuming that a rock was originally entirely uranium and that at present, 1.5% of the nuclei are now lead, calculate the age of the rock. Give your answer in years to 2 significant figures.

5c
Sme Calculator
3 marks

The ionisation current I produced by α-particles emitted in the decay of radon can be measured experimentally. The logarithmic graph shows how current, ln I, varies with time, t.

9Ny8MkHj_12-2-ib-hl-sqs-hard-q5b-question

Using the graph, determine the half-life of radon.

Did this page help you?

6a
Sme Calculator
2 marks

Unstable uranium-238 has various nuclear decay modes to become stable thorium-234. The total amount of energy released when it decays is measured to be 210 keV. 

q1b

 

Outline, without calculation, the intermediate decay modes between the unstable uranium-238 to the stable thorium-234. 

6b
Sme Calculator
4 marks

A possible decay chain for uranium-238 is: 

U presubscript 92 presuperscript 238 blank rightwards arrow blank scriptbase T h to the power of asterisk times end scriptbase presubscript 90 presuperscript 234 italic space plus blank scriptbase alpha blank end scriptbase presubscript 2 presuperscript 4

scriptbase T h to the power of asterisk times end scriptbase presubscript 90 presuperscript 234 blank rightwards arrow blank scriptbase T h to the power of asterisk times end scriptbase presubscript 90 presuperscript 234 italic space plus space gamma

scriptbase T h to the power of asterisk times end scriptbase presubscript 90 presuperscript 234 blank rightwards arrow blank scriptbase T h end scriptbase presubscript 90 presuperscript 234 italic space plus space gamma

Calculate the total amount of energy, in joules, carried away as gamma radiation in this decay chain. 

6c
Sme Calculator
2 marks

Deduce an alternative decay chain from unstable uranium-238 to stable thorium-234 which releases the same amount of energy in the form of gamma radiation as in part (b). 

Justify your answer with a calculation. 

Did this page help you?

7a
Sme Calculator
3 marks

The half-life of uranium-238 is so long in comparison to any of the isotopes in its decay chain that we can assume the number of lead-206 nuclei, N subscript P b end subscript at any time is equal to the number of uranium-238 that have decayed. 

The number of uranium-238 nuclei N subscript U at time t is given by the equation: 

N subscript U space equals space N subscript 0 e to the power of negative lambda t end exponent

Where N subscript 0 is the number of uranium-238 nuclei at t = 0.

Show that the ratio of N subscript P b end subscript to N subscript U is given by:

N subscript P b end subscript over N subscript U space equals space e to the power of lambda t end exponent space minus space 1
7b
Sme Calculator
3 marks

Enriched uranium fuel is a mixture of the fissionable uranium-235 with the more naturally abundant uranium-238. Mixtures of radioactive nuclides such as this are very common in the nuclear power industry. 

Two samples of radioactive nuclides X and Y each have an activity of A0 at t = 0. They are subsequently mixed together. 

The half-lives of X and Y are 16 and 8 years respectively. 

Show that the total activity of the mixture at time t = 48 years is equal to:

 
9 over 64 A subscript 0

Did this page help you?