Syllabus Edition

First teaching 2014

Last exams 2024

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Nuclear Reactions (DP IB Physics: HL)

Topic Questions

3 hours45 questions
1a
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2 marks

Define unified atomic mass unit.

1b
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3 marks

The unified atomic mass unit (a.m.u) is roughly equal to the mass of one nucleon.

Calculate the mass of a nucleus of uranium−238. Give your answer to 3 significant figures.

You may take 1 a.m.u to be 1.66 × 10−27 kg.

1c
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3 marks

Einstein's Theory of Relativity showed that mass could be converted into energy, and energy into mass. This is summarised in the equation:

straight capital delta E equals straight capital delta m c squared

Define the terms in the equation and give the units:

 
(i)
E
[1]
(ii)
m
[1]
(iii)
c
[1]
1d
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2 marks

Calculate the energy (in J) released if all of the mass in the nucleus of uranium−238 were converted into energy.

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2a
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2 marks

Define: 

(i)
Binding energy.
[1]
(ii)
Mass defect.
[1]
2b
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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.

2c
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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

2d
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2 marks

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

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3a
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2 marks

The binding energy per nucleon of Helium−4 open parentheses He presubscript 2 presuperscript 4 close parentheses is 7.1 MeV.

Determine the energy required to completely separate the nucleons of the atom of helium. Give your answer in MeV.

3b
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2 marks

Match the processes with the correct definition by drawing a line:

7-2b
3c
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3 marks

Complete the following sentences using appropriate words: 

Helium is formed inside main sequence stars due to the process of nuclear ________. For this process to occur, both nuclei must have high _______ energy. This high energy is because the protons inside the nuclei are ________ charged and a great deal of energy is needed to overcome the ________ force of repulsion.

3d
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2 marks

Complete the following sentences using appropriate words: 

Nuclear ________ can be induced by firing ________ at a nucleus. When the nucleus is struck it splits into two or more ________ nuclei and more ________. This leads to a chain reaction.

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4a
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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]
(ii)
The location of Iron open parentheses Fe presubscript 26 presuperscript 56 close parentheses by drawing an X
[1]
4b
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4 marks

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

(i)
Fusion occurs for nuclides with low nucleon numbers.
[2]
(i)
Fission occurs for nuclides with high nucleon numbers.
[2]
4c
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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.

4d
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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]

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5a
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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
5b
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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.

5c
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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]
5d
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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.

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1a
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2 marks

A nuclear fission reaction occurs that has the following equation:

                               n presubscript 0 presuperscript 1 plus U presubscript 92 presuperscript 235 rightwards arrow S presubscript 38 presuperscript 90 r plus X presubscript 54 presuperscript 143 e plus 3 n presubscript 0 presuperscript 1 

Given the following information, estimate the amount of energy released during the fission reaction:                             

  • Binding energy per nucleon of Uranium 235: 7.59 MeV/nucleon
  • Binding energy per nucleon of Strontium 90: 8.70 MeV/nucleon
  • Binding energy per nucleon of Xenon-143: 8.20 MeV/nucleon
1b
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4 marks

The binding energy per nucleon curve is shown:                      q1b_7-2_medium_ibphysics

With reference to the binding energy per nucleon curve:

 
(i)
Explain why fission is possible
[2]
(ii)
Identify the source of energy released during this process

[2]

1c
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5 marks

A Uranium-235 nucleus undergoes fission into two approximately equally sized products.        

Use the data from the figure in part (b) to show that the energy released as a result of the fission is approximately 4 × 10−11 J. 

Show on the graph how you have used the data.

1d
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4 marks

Under the right conditions, two hydrogen-2, 2H, nuclei can fuse to make a helium-4, 4He, nucleus.

    
Nuclei Mass/ u
H presuperscript 2 2.0135
H presuperscript 4 e 4.0026

Using the data in the above table, calculate the energy available as a result of the fusion of two hydrogen-2 nuclei.

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2a
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2 marks

This question is about nuclear physics. 

(i)
Define mass defect 

(ii)
Define binding energy
2b
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2 marks

If deuterium is combined using fusion, then the following reaction will occur: 

                                               H presubscript 1 presuperscript 2 plus H presubscript 1 presuperscript 2 rightwards arrow H presubscript 1 presuperscript 3 plus H presubscript 1 presuperscript 1

The following data is given for this interaction: 

  •    Binding energy per nucleon of deuterium H presubscript 1 presuperscript 2 : 1.12 MeV/nucleon
  •    Binding energy per nucleon of tritium H presubscript 1 presuperscript 3 : 2.82 MeV/nucleon

Estimate the energy released from this fusion reaction.

2c
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2 marks

In order for the fusion reaction in part (b) to actually take place, very high temperatures are needed such as those found within the core of a star. Suggest why this the case.

2d
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3 marks

Fission and fusion reactions release different amounts of energy. 

Discuss other reasons why it would be preferable to use fusion rather than fission for the production of electricity, assuming that the technical problems associated with fusion can be overcome. 

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3a
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3 marks

The image below shows how the binding energy per nucleon varies 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 image, 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]
3b
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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.

3c
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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).

3d
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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]

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4a
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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.

4b
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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

4c
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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
4d
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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.

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5a
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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.

5b
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2 marks

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

5c
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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.

5d
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3 marks

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

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1a
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3 marks

During a particular fission process, a uranium–236 nucleus is bombarded with a slow-moving neutron creating a krypton–92 nucleus and a barium–141 nucleus, among other fission products. 

The graph shows the relationship between the binding energy per nucleon and the mass number for various nuclides.

7-2-ib-sl-hard-sqs-q1a-question

Calculate the energy released during this fission process.

1b
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2 marks

Identify the other fission products in this process and justify why they can be discounted from the calculation in part (a). 

1c
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5 marks

A different fission process, involving uranium–235 is again triggered by the absorption of a slow−moving neutron and releases gamma ray photons. The process is described by the equation below: 

straight U presubscript 92 presuperscript 235 space plus space straight n presubscript 0 presuperscript 1 space rightwards arrow space Te presubscript 52 presuperscript 138 space plus space Zr presubscript 40 presuperscript 98 space plus space straight gamma

In this process, 90% of the energy released is carried away as kinetic energy of the two daughter nuclei.

The following data are available:

  • Mass of straight U presubscript 92 presuperscript 235 space= 235.0439 u
  • Mass of Te presubscript 52 presuperscript 138 = 137.9603 u
  • Mass of Zr presubscript 40 presuperscript 98 = 97.9197 u
  • Mass of straight n presubscript 0 presuperscript 1 = 1.0087 u
  • Wavelength of gamma photons emitted = 2.5 × 10–12 m

Show that approximately 32 gamma ray photons are released in this process.

1d
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2 marks

Assuming the nuclei are initially at rest, show that the Zr presubscript 40 presuperscript 98 nucleus is emitted with a speed about 1.4 times larger than the Te presubscript 52 presuperscript 138 nucleus.

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2a
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5 marks

When a uranium–235 nucleus undergoes fission, one of the possible reactions is: 

straight U presubscript 92 presuperscript 235 space plus space straight n presubscript 0 presuperscript 1 rightwards arrow Xe presubscript 54 presuperscript 139 space plus space Sr presubscript 38 presuperscript 95 space plus space 2 straight n presubscript 0 presuperscript 1 space left parenthesis plus energy right parenthesis

The binding energy per nucleon, E, is given in the table below: 

Nuclide E/MeV
straight U presubscript 92 presuperscript 235 7.60
Xe presubscript 54 presuperscript 139 8.39
Sr presubscript 38 presuperscript 95 8.74

A 1500 MW nuclear reactor, operating at 27% efficiency, uses enriched fuel containing 2% uranium–235 and 98% uranium–238. The molar mass of uranium−235 is 0.235 kg/mol.

Estimate the total mass of original fuel required per year in the nuclear reactor. 

2b
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2 marks

The average energy released by the various modes of fission of uranium–235 is 200 MeV. 

Calculate the number of fission reactions per day in the nuclear reactor (assuming continuous production of power). 

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3a
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5 marks

In the research into nuclear fusion, scientists are working with 1.5 kg of Lithium. One of the most promising reactions is between deuterons, H presubscript 1 presuperscript 2, and tritium nuclei,H presubscript 1 presuperscript 3, in a gaseous plasma. Although deuterons can be relatively easily extracted from sea water, tritium is more difficult to produce. It can, however, be produced by bombarding lithium−6, Li presubscript 3 presuperscript 6 , with neutrons. 

These reactions can be represented in the following nuclear equations:

straight H presubscript 1 presuperscript 2 plus straight H presubscript 1 presuperscript 3 rightwards arrow He presubscript 2 presuperscript 4 plus straight n presubscript 0 presuperscript 1 plus left parenthesis energy right parenthesis

Li presubscript 3 presuperscript 6 plus straight X rightwards arrow straight H presubscript 1 presuperscript 3 plus straight Y plus left parenthesis energy right parenthesis

The masses of the nuclei involved are given in the following table:

Nuclei Mass / u

Neutron

1.008665

Deuteron

2.013553

Tritium

3.016049

Helium−4

4.002603

Lithium−6

6.015122

 
(i)
Determine the nature of particles X and Y and hence complete the equation.
  [1]
(ii)
Calculate the maximum amount of energy, in MeV, released when 1.5 kg of lithium-6 is bombarded by neutrons.
[4]
3b
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2 marks

Suggest why the lithium-6 reaction could be thought to be self-sustaining once the deuteron-tritium reaction is underway.

3c
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3 marks

Explain, in terms of the forces acting on nuclei, why the deuteron-tritium mixture must be very hot in order to achieve the fusion reaction.

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4a
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3 marks

This is a synoptic question and will need knowledge from previous IB topics.

Plasma is superheated matter. It is so hot that the electrons are stripped from their atoms, forming an ionised gas. 

The Sun is made up of gas and plasma and can be thought of as a giant fusion reactor. At its core where fusion takes place, the plasma is (mainly) protons with a temperature of about 1.5 × 106 K.

Near the Sun's surface, however, protons have a mean kinetic energy of 0.75 eV, which is too low for fusion to take place.

Calculate the temperature of the Sun near its surface, stating any assumptions you make.

4b
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4 marks

By considering the distance of closest approach between two protons, explain why fusion does not occur near the Sun’s surface.

4c
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4 marks

The energy produced by the Sun comes from a cycle of hydrogen fusion, during which the net effect is the fusion of 3 protons to a helium nucleus. One of the steps in the cycle is:

straight H presubscript 1 presuperscript 1 space plus space straight H presubscript 1 presuperscript 2 rightwards arrow He presubscript 2 presuperscript 3 space plus space left parenthesis energy right parenthesis

The amount of energy radiated away in this step is 5.49 MeV. 

The following data are available:

  • Mass of H presubscript 1 presuperscript 2 nucleus = 2.01355 u
  • Mass of proton = 1.00728 u  
(i)
Calculate the mass of the helium nucleus, He presubscript 2 presuperscript 3 in standard units
 [3]
(ii)
State the nature of the energy released
[1]

   

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5a
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4 marks

One possible fission reaction of uranium-235 is

straight U presubscript 92 presuperscript 235 space plus space straight n presubscript 0 presuperscript 1 space rightwards arrow space Xe presubscript 54 presuperscript 140 space plus space Sr presubscript 38 presuperscript 94 space plus space 2 straight n presubscript 0 presuperscript 1

The following data are available:

  • Mass of one atom of U presubscript 92 presuperscript 235 = 235u
  • Binding energy per nucleon for straight U presubscript 92 presuperscript 235 = 7.59 MeV
  • Binding energy per nucleon for Xe presubscript 54 presuperscript 140 = 8.29 MeV
  • Binding energy per nucleon for Sr presubscript 38 presuperscript 94 = 8.59 MeV

Calculate the amount of energy released in the reaction.

5b
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5 marks

A nuclear power station uses the uranium-235 as fuel. The useful power output of the power station is 1.4 GW and it has an efficiency of 30%.

 
(i)
Show that the specific energy of straight U presubscript 92 presuperscript 235 is about 7.5 × 1013 J kg−1.
[3]
(ii)
Determine the mass of U presubscript 92 presuperscript 235 which undergoes fission in one day.
[2]
5c
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4 marks

One of the waste products of the reaction is xenon−140, Xe presubscript 54 presuperscript 140. Xenon−140 is radioactive, decaying through beta to the power of minus decay.

Xe presubscript 54 presuperscript 140 rightwards arrow straight Z space plus space straight beta to the power of minus plus stack straight nu subscript straight 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]
5d
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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.

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