Nuclear fission and fusionEdexcel A-Level Physics: Subtopic test

1. 1
   The binding energy per nucleon of nuclei varies with nucleon number. It rises steeply for the lightest nuclei, reaches a maximum of about 8.8 MeV per nucleon at a nucleon number of about 56 (iron-56), and then falls slowly for heavier nuclei, to about 7.6 MeV per nucleon for uranium-235.

   (a)

   Which one of these processes would release energy?

   [1 mark]

   • AFusion of two deuterium nuclei to form a helium-4 nucleus
   • BFission of an iron-56 nucleus into two lighter nuclei
   • CFusion of two uranium-235 nuclei into one heavier nucleus
   • DFission of a helium-4 nucleus into two deuterium nuclei

   (b)

   Why is energy released when a nucleus of uranium-235 undergoes fission?

   [1 mark]

   • AThe fission fragments have a lower binding energy per nucleon than uranium-235
   • BThe fission fragments have a greater total number of nucleons
   • CThe fission fragments have a higher binding energy per nucleon than uranium-235
   • DUranium-235 has the highest binding energy per nucleon of any nucleus

   (c)

   Use the information about the binding energy per nucleon to explain why energy is released when two light nuclei fuse.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a proposed fusion reactor, a gas of deuterium (hydrogen-2) and tritium (hydrogen-3) nuclei is heated until it forms a plasma at a temperature of about $1 \times 10^{8}$ K. The nuclei are then held together at a very high density so that they can fuse to form helium-4.

   (a)

   Why do the nuclei need a very high temperature before they can fuse?

   [1 mark]

   • ANeutrons in the nuclei repel each other and have to be removed
   • BThe positively charged nuclei repel each other, so they need enough kinetic energy to get close enough for the strong force to act
   • CThe nuclei have to be vaporised before they can collide
   • DGravity pulls the nuclei apart at low temperatures

   (b)

   Which of these is the equation for fusion of deuterium and tritium to form helium-4?

   [1 mark]

   • A${}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{3}_{2}\text{He} + {}^{1}_{0}\text{n}$
   • B${}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{1}\text{p}$
   • C${}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{0}_{-1}\text{e}$
   • D${}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n}$

   (c)

   Explain why fusion requires both a very high temperature and a very high density.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a nuclear power station, one of the fission reactions of uranium-235 is ${}^{1}_{0}\text{n} + {}^{235}_{92}\text{U} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3\,{}^{1}_{0}\text{n}$. Binding energy per nucleon: uranium-235, 7.59 MeV; barium-141, 8.33 MeV; krypton-92, 8.51 MeV. Take $1\text{ MeV} = 1.60 \times 10^{-13}$ J, the molar mass of uranium-235 as 235 g mol⁻¹ and $N_A = 6.02 \times 10^{23}$ mol⁻¹.

   (a)

   Use the binding energy per nucleon values to calculate the energy released, in MeV, when one uranium-235 nucleus undergoes this fission.

   [3 marks]

   (b)

   Calculate the energy released, in J, when 1.0 g of uranium-235 undergoes fission in this way.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A newspaper article compares fission in nuclear power stations with the fusion reactors that are being developed. Binding energy per nucleon: hydrogen-2, 1.1 MeV; helium-4, 7.1 MeV; uranium-235, 7.6 MeV; typical fission fragments, about 8.5 MeV. The core of the Sun is at about $1.5 \times 10^{7}$ K and has a density of about $1.5 \times 10^{5}$ kg m⁻³. An experimental fusion reactor on Earth must heat its fuel to about $1 \times 10^{8}$ K and works at a density that is far lower than that in the Sun's core.

   (a)

   Explain, with reference to the binding energy per nucleon curve, why energy is released in both fission and fusion. Use the data to compare the energy released per nucleon in the two processes.

   [6 marks]

   (b)

   Explain why fusion needs a very high temperature and density, and evaluate why it is much harder to achieve a net energy gain from fusion on Earth than it is in the Sun.

   [6 marks]

   Total for question 4: 12 marks

End of questions