CAIE A-Level Physics A2 23.1 Mass Defect and Nuclear Binding Energy Questions

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

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

[Maximum number: 10]

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

{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{42}^{95} \mathrm{Mo}+{ }_{57}^{139} \mathrm{La}+2{ }_{0}^{1} \mathrm{n}+\ldots \ldots \ldots \ldots .+ \text { energy }

Data for a nucleus and some particles are given in Fig. 12.1.

Fig. 12.1

(a)

Complete the nuclear reaction shown above.

[ 1 ]

$7{ }_{-1}^{0} \mathrm{e}$

(b)

Show that the energy equivalent to 1.00 u is 934 MeV .

[ 3 ]

$E=m c^{2}$ $=1.66 \times 10^{-27} \times\left(3.00 \times 10^{8}\right)^{2}$ $=1.494 \times 10^{-10} \mathrm{~J}$

division by $1.60 \times 10^{-13}$ clear to give 934 MeV

(c)

Calculate the binding energy per nucleon, in MeV , of lanthanum-139 $\left({ }_{57}^{139} \mathrm{La}\right)$ . MeV

[ 3 ]

$\begin{aligned} \Delta m =(82 \times 1.00863 u)+(57 \times 1.00728 u)-138.955 u =(-) 1.16762(u) \end{aligned}$
energy $=1.16762 \times 934$
energy per nucleon $=(1.16762 \times 934) / 139$ $=7.85 \mathrm{MeV}$

(d)

State and explain whether the binding energy per nucleon of uranium-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ will be greater, equal to or less than your answer in (b)(ii).

[ 3 ]

[Maximum number: 10]

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

Table 9.1

(a)

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

Complete the equation.

{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{42}^{95} \mathrm{Mo}+{ }_{57}^{139} \mathrm{La}+2{ }_{0}^{1} \mathrm{n}+\ldots \ldots \ldots \ldots \ldots \ldots \ldots .+ \text { energy } .

[ 2 ]

$7_{-1}^{0} \mathrm{e}$

B1

(b)

Show that the energy equivalent to 1.00 u is 934 MeV .

[ 3 ]

$E=m c^{2}$ $E=1.66 \times 10^{-27} \times\left(3.00 \times 10^{8}\right)^{2}$

( $=1.494 \times 10^{-10} \mathrm{~J}$ )
division of energy by $1.60 \times 10^{-13}$ shown, to give 934 MeV

(c)

Calculate the binding energy per nucleon, in MeV , of lanthanum-139 $\left({ }_{57}^{139} \mathrm{La}\right)$ .
binding energy per nucleon = MeV

[ 3 ]

$\begin{aligned} \Delta m=(82 \times 1.00863 u)+(57 \times 1.00728 u)-138.955 u \Delta m=(-) 1.16762(u) \end{aligned}$
energy $=1.16762 \times 934$
energy per nucleon $=(1.16762 \times 934) / 139$

=7.85 MeV

(d)

State and explain whether the binding energy per nucleon of uranium-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ is greater, equal to or less than the binding energy per nucleon of lanthanum-139 $\left({ }_{57}^{139} \mathrm{La}\right)$ .

[ 2 ]

[Maximum number: 1]

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

{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{42}^{95} \mathrm{Mo}+{ }_{57}^{139} \mathrm{La}+2{ }_{0}^{1} \mathrm{n}+\ldots \ldots \ldots \ldots .+ \text { energy }

Data for a nucleus and some particles are given in Fig. 12.1.

Fig. 12.1

Complete the nuclear reaction shown above.

$7{ }_{-1}^{0} \mathrm{e}$

[Maximum number: 3]

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

Table 9.1

Calculate the binding energy per nucleon, in MeV , of lanthanum-139 $\left({ }_{57}^{139} \mathrm{La}\right)$ .
binding energy per nucleon = MeV

[Maximum number: 3]

(a)

On Fig. 9.1, sketch the variation with nucleon number A of binding energy per nucleon for values of A from 1 to 250.

Fig. 9.1

[ 2 ]

(b)

On your line in Fig. 9.1, draw an X to show the approximate position of polonium-212.

[ 1 ]

[Maximum number: 2]

State what is meant by nuclear fusion.

[Maximum number: 2]

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} .

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

[Maximum number: 2]

A nucleus of uranium-235 absorbs a neutron and becomes unstable. It then undergoes a fission reaction. One possible reaction is

{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{54}^{142} \mathrm{Xe}+{ }_{38}^{90} \mathrm{Sr}+\text { neutrons. }

Data for the binding energies per nucleon for this fission reaction are given in Table 8.1.

Table 8.1

Calculate the energy released, in MeV , from the fission of one nucleus of uranium-235. MeV

energy $=(142 \times 8.37)+(90 \times 8.72)-(235 \times 7.59)$
=190 MeV

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Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question 3

Question (a)

Question (b)

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Question (d)

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Question 6

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Question 9