Mass Defect & Nuclear Binding Energy (Cambridge (CIE) A Level Physics): Exam Questions

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

Table 9.1

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

Complete the equation.

(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 ( ${}_{57}{}^{139}\mathrm{La}$).

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

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

(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.

Fig. 1.1

[2]

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

[2]

A nuclear fission reaction occurs that has the following equation 

${}_0{}^1\mathrm{n}+{}_{92}{}^{235}\mathrm{U}\to {}_{38}{}^{90}\mathrm{Sr}+{}_{54}{}^{143}\mathrm{Xe}+x{}_0{}^1\mathrm{n}$

(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

[2]

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

Table 1.3

(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]

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

${}^2\mathrm{H}+{}^2\mathrm{H}\to {}^4\mathrm{He}$

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

Define the terms 

(i) mass defect

[1]

(ii) binding energy of a nucleus.

[2]

If deuterium $\left({}_1{}^2\mathrm{H}\right)$ nuclei undergo fusion, a possible reaction is

${}_1{}^2\mathrm{H}+{}_1{}^2\mathrm{H}\to {}_1{}^3\mathrm{H}+{}_1{}^1\mathrm{H}$

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

Table 1.1

(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]

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

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]

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.

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. 

Fig. 1.1

Using Fig. 1.1, calculate the energy released during this fission process.

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

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: 

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{52}{}^{138}\mathrm{Te}+{}_{40}{}^{98}\mathrm{Zr}+\mathrm{\gamma }$

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 ${}_{92}{}^{235}\mathrm{U}$ = 235.0439u

Mass of ${}_{52}{}^{138}\mathrm{Te}$ = 137.9603u

Mass of ${}_{40}{}^{98}\mathrm{Zr}$ = 97.9197u

Mass of ${}_0{}^1\mathrm{n}$ = 1.0087u

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

Assuming the uranium nucleus is initially at rest, show that the ${}_{40}{}^{98}\mathrm{Zr}$ nucleus is emitted with a speed about 1.4 times larger than the ${}_{52}{}^{138}\mathrm{Te}$ nucleus.

When a uranium–235 nucleus undergoes fission, one possible reaction is:

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{54}{}^{139}\mathrm{Xe}+{}_{38}{}^{95}\mathrm{Sr}+2{}_0{}^1\mathrm{n}+\mathrm{energy}$ 

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

Table 1.1

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).  

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

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.