Mass, energy and binding energyAQA A-Level Physics: Subtopic test

1. 1
   A student is analysing the helium-4 nucleus using these data: nuclear mass of helium-4 = 4.00151 u; mass of a proton = 1.00728 u; mass of a neutron = 1.00867 u; 1 u = 931.5 MeV.

   (a)

   What is the mass defect of the helium-4 nucleus?

   [1 mark]

   • A0.01520 u
   • B0.06078 u
   • C0.03039 u
   • D4.03190 u

   (b)

   What is the average binding energy per nucleon of helium-4?

   [1 mark]

   • A7.08 MeV
   • B28.3 MeV
   • C14.2 MeV
   • D3.54 MeV

   (c)

   Explain why the mass of a helium-4 nucleus is less than the total mass of its separate nucleons.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A power station burns coal. Burning 1.0 kg of coal releases 3.0 × 10⁷ J of energy. The speed of light in a vacuum is c = 3.00 × 10⁸ m s⁻¹.

   (a)

   What is the decrease in the mass of the system when 1.0 kg of coal is burned?

   [1 mark]

   • A1.0 × 10⁻¹ kg
   • B3.3 × 10⁻¹⁰ kg
   • C2.7 × 10²⁴ kg
   • D3.0 × 10⁷ kg

   (b)

   Which statement about the mass of the products of the combustion, compared with the reactants, is correct?

   [1 mark]

   • AThe masses are exactly equal, because mass is always conserved in chemical reactions.
   • BThe products have a greater total mass, because energy has been released.
   • CThe mass changes only in nuclear reactions, not in chemical ones.
   • DThe products have a slightly smaller total mass, because energy has left the system.

   (c)

   Suggest why the mass change in a chemical reaction is never noticed, but the mass change in a nuclear reaction can be measured.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Average binding energy per nucleon: hydrogen-2 (deuterium) 1.1 MeV; helium-4 7.1 MeV; iron-56 8.8 MeV; uranium-235 7.6 MeV. When a uranium-235 nucleus undergoes fission, the fragments formed have an average binding energy per nucleon of 8.5 MeV. 1 MeV = 1.60 × 10⁻¹³ J.

   (a)

   Explain, in terms of binding energy per nucleon, why energy is released both when light nuclei such as hydrogen-2 fuse and when heavy nuclei such as uranium-235 undergo fission.

   [3 marks]

   (b)

   Calculate the energy released, in joules, when one nucleus of uranium-235 undergoes fission into fragments with a total of 235 nucleons. Ignore any free neutrons.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A research team is assessing fusion as a future energy source. In the fusion of deuterium and tritium, ²H + ³H → ⁴He + ¹n. Nuclear masses: deuterium 2.01355 u; tritium 3.01550 u; helium-4 4.00151 u; neutron 1.00867 u. 1 u = 931.5 MeV = 1.661 × 10⁻²⁷ kg; 1 MeV = 1.60 × 10⁻¹³ J. For comparison, the fission of uranium-235 releases about 0.9 MeV per nucleon of the nucleus.

   (a)

   Calculate the energy released, in joules, when one deuterium nucleus fuses with one tritium nucleus, and the energy released per kilogram of the reactants.

   [6 marks]

   (b)

   The deuterium–tritium reaction releases 17.6 MeV. Compare the energy released per nucleon in this fusion reaction with that in the fission of uranium-235. Explain, using how average binding energy per nucleon varies with nucleon number, why fusion releases more energy per nucleon than fission, and why fusing nuclei heavier than iron-56 would not release energy.

   [6 marks]

   Total for question 4: 12 marks

End of questions