CAIE A-Level Physics Nuclear Binding Overview

Practise calculating mass defect and nuclear energy, completing equations, interpreting binding-energy curves and comparing fission, fusion and decay.

Exam points

calculate mass-energy equivalence using E = mc� and explain mass changes in nuclear reactions
complete and interpret nuclear equations by conserving nucleon and proton numbers
define and calculate mass defect and binding energy
interpret the binding-energy-per-nucleon curve to compare nuclei and distinguish fusion from fission
calculate energy released from mass change or binding-energy change and convert between joules and electronvolts

Covered syllabus points

23.1.1—The equivalence between energy and mass as represented by E = mc 2 and 23.1.2—Simple nuclear reactions by nuclear equations of the form NH eO H7 14 2 4 8 23.1.3—The terms mass defect and binding energy 23.1.4—The variation of binding energy per nucleon with nucleon number 23.1.5—What is meant by nuclear fusion and nuclear fission 23.1.6—The relevance of binding energy per nucleon to nuclear reactions 23.1.7—The energy released in nuclear reactions using E = c 2∆m

[Maximum number: 1]

Use data from (b) to calculate the mass that is converted into energy every second in the Sun.
mass = kg

$\begin{aligned} m=\frac{E}{c^{2}} =\frac{3.83 \times 10^{26}}{3.00 \times 10^{82}} =4.26 \times 10^{9} \mathrm{~kg} \end{aligned}$

A1

[Maximum number: 10]

(a)

State what is meant by nuclear fusion and nuclear fission.
nuclear fusion:
nuclear fission:

[ 3 ]

(b)

A nuclear reaction which may, in the future, be used for the generation of electrical energy is

{ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+\mathrm{x} .

[ 7 ]

(i)

Name the particle x .

[ 1 ]

(ii)

Data for the binding energy per nucleon $E_{\mathrm{B}}$ of some nuclei are given in Fig. 12.1.

Fig. 12.1

1. State the binding energy per nucleon of x .

binding energy per nucleon =J

2. Calculate the energy change that takes place in this reaction.

energy change =

[ 3 ]

1. zero

A1

2. $\left(4 \times 11.3290 \times 10^{-13}\right)-\left(2 \times 1.7813 \times 10^{-13}\right)-\left(3 \times 4.5285 \times 10^{-13}\right)$

C1

$\begin{aligned} \text { energy change } =45.316 \times 10^{-13}-17.148 \times 10^{-13} =2.82 \times 10^{-12} \mathrm{~J} \end{aligned}$

A1

(iii)

Use your answer in (ii) part 2 to determine the energy release when 2.0 g of deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ reacts with 3.0 g of tritium $\left({ }_{1}^{3} \mathrm{H}\right)$ .

energy =

[ 3 ]

1.0 mol or $N_{\mathrm{A}}$ nuclei of each
$\begin{aligned} \text { energy } =2.817 \times 10^{-12} \times 6.02 \times 10^{23} =1.7 \times 10^{12} \mathrm{~J} \end{aligned}$

A1

[Maximum number: 12]

(a)

State what is meant by nuclear binding energy.

[ 2 ]

(b)

On Fig. 8.1, sketch a line to show the variation with nucleon number A of the binding energy per nucleon E of a nucleus.

Fig. 8.1

[ 2 ]

(c)

In one type of nuclear process, deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ undergoes the reaction

{ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n} .

[ 3 ]

(i)

State the name of this type of nuclear process.

[ 1 ]

(ii)

Explain, with reference to your line in (a)(ii), why this reaction results in the release of energy.

[ 2 ]

(d)

Table 8.1 shows the masses of the particles involved in the reaction in (b).

Table 8.1

Calculate the energy released when 1.00 mol of deuterium undergoes the reaction. J

[ 5 ]

$\begin{aligned} \Delta m =[(2 \times 2.014102)-(3.016029+1.008665)] \mathrm{u} (=0.00351 \mathrm{u}) \end{aligned}$

C1

$E=\Delta m c^{2}$

C1

$\begin{aligned} =0.00351 \times 1.66 \times 10^{-27} \times\left(3.00 \times 10^{8}\right)^{2} \left(=5.24 \times 10^{-13} \mathrm{~J}\right) \end{aligned}$

C1

1.00 mol of deuterium forms 0.500 mol of helium-3

C1

$\begin{aligned} \text { total energy } =0.500 \times 6.02 \times 10^{23} \times 5.24 \times 10^{-13} =1.58 \times 10^{11} \mathrm{~J} \end{aligned}$

A1

All question bank results loaded

Covered syllabus points

23.1 Mass defect and nuclear binding energy question 1

23.1 Mass defect and nuclear binding energy question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

23.1 Mass defect and nuclear binding energy question 3

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (d)