Syllabus Edition

First teaching 2023

First exams 2025

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Mass Defect & Nuclear Binding Energy (CIE A Level Physics)

Exam Questions

2 hours8 questions
1a
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2 marks

Define atomic mass unit.

1b
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3 marks

The unified atomic mass unit u is roughly equal to 1.66 × 10−27 kg which is the mass of one nucleon.

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

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 by the following equation

increment E space equals space increment 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 released, in J, 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

State the meaning of the terms 

(i)
binding energy,
[1]
(ii)
mass defect.
[1]
2b
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5 marks

The nuclear rest mass m subscript t o t a l end subscript of oxygen−16 open parentheses straight O presubscript 8 presuperscript 16 close parentheses is 15.994914 u. 

The following equation describes the relationship between mass defect increment m and the mass of the constituents of a nucleus

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

(i)
State the meaning of the terms Z m subscript p and N m subscript n.
[2]
(ii)
Calculate the mass defect of oxygen−16.
 
m subscript p = 1.007276 u
m subscript n = 1.008665 u
[3]

2c
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3 marks

Use the mass defect from (b) to show that the total binding energy of a nucleus of oxygen−16 is about 2 × 10−11 J.

2d
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4 marks

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

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3a
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3 marks

Fig. 1.1 shows the binding energy per nucleon for a number of nuclei.

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

Fig. 1.1

On Fig. 1.1, mark

  • the region in which fusion occurs
  • the region in which fission occurs
  • an X to show the location of iron-56 open parentheses Fe presubscript 26 presuperscript 56 close parentheses

3b
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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]
(ii)
fission occurs for nuclides with high nucleon numbers.
[2]
3c
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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.

3d
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3 marks

The graph in Fig. 1.2 shows the binding energy per nucleon in MeV plotted against nucleon number, A.

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

Fig. 1.2

Use Fig. 1.2 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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1a
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1 mark

Data for a nucleus and some particles are given in Table 9.1.

Table 9.1

nucleus or particle mass / u
La presubscript 57 presuperscript 139 138.955
straight n presubscript 0 presuperscript 1 1.00863
straight p presubscript 1 presuperscript 1 1.00728
e presubscript negative 1 end presubscript presuperscript 0 5.49 × 10–4

 

One nuclear reaction that can take place in a nuclear reactor may be represented, in part, by the equation shown below.

Complete the equation.

straight U presubscript 92 presuperscript 235 space plus space straight n presubscript 0 presuperscript 1 space rightwards arrow with blank on top space Mo presubscript 42 presuperscript 95 space plus space La presubscript 57 presuperscript 139 space plus space 2 straight n presubscript 0 presuperscript 1 space plus space................ plus energy

1b
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6 marks
(i)
Show that the energy equivalent to 1.00 u is 934 MeV.

[3]

(ii)
Calculate the binding energy per nucleon, in MeV, of lanthanum-139 ( La presubscript 57 presuperscript 139).



binding energy per nucleon = ..................................... MeV [3]

1c
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2 marks

State and explain whether the binding energy per nucleon of uranium-235 ( begin mathsize 16px style U presubscript 92 presuperscript 235 end style ) is greater, equal to or less than the binding energy per nucleon of lanthanum-139 ( begin mathsize 16px style La presubscript 57 presuperscript 139 end style ).

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2a
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5 marks
(i)
State what is meant by nuclear fission.

[1]

(ii)
On Fig. 1.1 below, sketch a line to show the variation with nucleon number A of the binding energy per nucleon E of a nucleus.

23-1-2a-m-23-1-binding-energy-per-nucleon-curve-blank-cie-ial-sq

Fig. 1.1

[2]

(iii)
Explain, with reference to Fig. 1.1, why nuclear fission reactions result in the release of energy.

[2]

2b
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3 marks

A nuclear fission reaction occurs that has the following equation 

straight n presubscript 0 presuperscript 1 space plus space straight U presubscript 92 presuperscript 235 space rightwards arrow space Sr presubscript 38 presuperscript 90 space plus space Xe presubscript 54 presuperscript 143 space plus space x straight n presubscript 0 presuperscript 1

(i)
Determine, for this nuclear reaction, the value of x.
[1]
(ii)
Data for the binding energy per nucleon of some nuclei are given in Table 1.2.
Use the data to calculate the energy, in MeV, released in this reaction.
 

Table 1.2

 

binding energy per nucleon / MeV

straight U presubscript 92 presuperscript 235

7.59

Sr presubscript 38 presuperscript 90

8.70

Xe presubscript 54 presuperscript 143

8.20

[2]

2c
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4 marks

Under the right conditions, a hydrogen-2 straight H presuperscript 2 nucleus can fuse with a hydrogen-1 straight H presuperscript 1 to make a helium-3 He presuperscript 3 nucleus. The values of binding energy per nucleon for these nuclei are shown in Table 1.3.

Table 1.3

Nuclei binding energy per nucleon / MeV
straight H presuperscript 2 0.864
He presuperscript 3 2.235
(i)
Write down the nuclear equation for this reaction.
[1]
(ii)
Explain why the binding energy per nucleon of hydrogen-1 is zero.
[1]
(iii)
Using the data in Table 1.3, calculate the energy released in this reaction.
[2]
2d
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4 marks

When two hydrogen-2 nuclei fuse into a helium-4 nucleus, 3.6 × 10−12 J of energy is released. This reaction is shown below

straight H presuperscript 2 space plus space straight H presuperscript 2 space rightwards arrow space He presuperscript 4

Show that the fusion of 1 kg of two hydrogen-2 nuclei releases about 8 times more energy per kg than the fission of 1 kg of uranium-235.

The masses of hydrogen-2 and uranium-235 are shown in Table 1.4.

  

Table 1.4

 

mass / u

straight H presubscript 1 presuperscript 2

2.013553

straight U presubscript 92 presuperscript 235

235.0439

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3a
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3 marks

Define the terms 

(i)
mass defect
[1]
(ii)
binding energy of a nucleus.
[2]
3b
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6 marks

If deuterium open parentheses straight H presubscript 1 presuperscript 2 close parentheses nuclei undergo fusion, a possible reaction is

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

The masses of the nuclei involved in the reaction are given in Table 1.1.
 

Table 1.1

 

mass / u

straight H presubscript 1 presuperscript 1

1.0078

straight H presubscript 1 presuperscript 2

2.0135

straight H presubscript 1 presuperscript 3

3.0160

(i)
Explain what is meant by nuclear fusion.
[1]
(ii)
Determine the energy released, in J, when 3.00 mol of deuterium undergoes this fusion reaction.
[5]
3c
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4 marks

Fig. 1.2 shows the variation of nucleon number with the binding energy per nucleon of a nucleus.

qu2c-fig-1

Fig. 1.2

With reference to Fig. 1.2, state and explain

(i)
which of the elements shown is the most stable
[2]
(ii)
how the graph can be used to predict whether a nucleus will undergo fusion or fission.
[2]
3d
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3 marks

Fission and fusion reactions release different amounts of energy.

Explain why the energy released per nucleon from fusion is greater than that from fission. State the feature of the graph in Fig. 1.2 that shows this.

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1a
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3 marks

During a particular fission process, a uranium-235 nucleus absorbs a slow-moving neutron to form uranium-236. This initiates the fission reaction, creating a krypton-92 nucleus and a barium-141 nucleus, among other fission products. 

Fig. 1.1 shows the relationship between the binding energy per nucleon and the mass number for various nuclides. 

8-4-s-q--q2a-hard-aqa-a-level-physics

Fig. 1.1

Using Fig. 1.1, 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 occurs. Fission of uranium-235 is triggered again by the absorption of a slow-moving neutron. Gamma-ray photons of wavelength 2.5 × 10–12 m are released. The process is described by the equation below: 

begin mathsize 20px style 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 end style

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

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

Mass of straight U presubscript 92 presuperscript 235 = 235.0439u

Mass of Te presubscript 52 presuperscript 138 = 137.9603u

Mass of Zr presubscript 40 presuperscript 98 = 97.9197u

Mass of straight n presubscript 0 presuperscript 1 = 1.0087u

You may use the fact that 1 u is the equivalent of 931.5 MeV c–2.

1d
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2 marks

Assuming the uranium nucleus is 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 possible reaction is:

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

The binding energy per nucleon E is given in Table 1.1 below: 

Table 1.1

nuclide

E / MeV

Sr presubscript 38 presuperscript 95

8.74

Xe presubscript 54 presuperscript 139

8.39

straight U presubscript 92 presuperscript 235

7.60

 

A nuclear reactor, operating at 27% efficiency, outputs 1500 MW. It uses enriched fuel containing 2% uranium–235 and 98% uranium–238. 

Estimate the total mass of original fuel required per year in the nuclear reactor (assume the molar mass of uranium-235 is 0.235 kg/mol).  

2b
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2 marks

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

2c
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3 marks

Hypothetically, nuclei larger than iron-56 can undergo fusion with enough energy. 

Explain why, even with enough energy, this could not be used as an energy resource.

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