CIE A Level Physics

Topic Questions

A LevelPhysicsCIETopic Questions23. Nuclear Physics23.1 Mass Defect & Nuclear Binding Energy

Syllabus Edition

First teaching 2020

Last exams 2024

|

23.1 Mass Defect & Nuclear Binding Energy

DownloadView
Easy
Medium
Easy
Medium
1a
Sme Calculator2 marks

Define atomic mass unit.

How did you do?

1b
Sme Calculator3 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.

How did you do?

1c
Sme Calculator3 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]

How did you do?

1d
Sme Calculator2 marks

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

How did you do?

Did this page help you?

2a
Sme Calculator2 marks

State the meaning of the terms 

(i)
binding energy,
[1]
(ii)
mass defect.
[1]

How did you do?

2b
Sme Calculator5 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]

How did you do?

2c
Sme Calculator3 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.

How did you do?

2d
Sme Calculator4 marks

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

How did you do?

Did this page help you?

3a
Sme Calculator3 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

How did you do?

3b
Sme Calculator4 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]

How did you do?

3c
Sme Calculator4 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.

How did you do?

3d
Sme Calculator3 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]

How did you do?

Did this page help you?

1a
Sme Calculator1 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

How did you do?

1b
Sme Calculator6 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]

How did you do?

1c
Sme Calculator2 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 ).

How did you do?

Did this page help you?

2a
Sme Calculator5 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]

How did you do?

2b
Sme Calculator3 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

U presubscript 92 presuperscript 235

7.59

Sr presubscript 38 presuperscript 90

8.70

Xe presubscript 54 presuperscript 143

8.20

[2]

How did you do?

2c
Sme Calculator4 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]

How did you do?

2d
Sme Calculator4 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

How did you do?

Did this page help you?

3a
Sme Calculator3 marks

Define the terms 

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

How did you do?

3b
Sme Calculator6 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]

How did you do?

3c
Sme Calculator4 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]

How did you do?

3d
Sme Calculator3 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.

How did you do?

Did this page help you?