Binding energy, fusion and fissionEdexcel International A Level Physics: Subtopic test

1. 1
   A student is analysing the helium-4 nucleus, which contains 2 protons and 2 neutrons. She is given the following data: mass of a proton = 1.00728 u; mass of a neutron = 1.00867 u; mass of a helium-4 nucleus = 4.00151 u.

   (a)

   Which statement correctly defines the mass deficit of the helium-4 nucleus?

   [1 mark]

   • AThe mass of the nucleus minus the total mass of its separate nucleons
   • BThe total mass of the separate nucleons minus the mass of the nucleus
   • CThe mass lost by the nucleus when it emits an alpha particle
   • DThe total mass of the electrons removed to form the nucleus

   (b)

   Which statement about the binding energy of the helium-4 nucleus is correct?

   [1 mark]

   • AIt is the energy released when the nucleus decays by alpha emission
   • BIt is the energy needed to turn all of its protons into neutrons
   • CIt is the total kinetic energy of the nucleons moving inside the nucleus
   • DIt is the minimum energy needed to separate the nucleus completely into its individual nucleons

   (c)

   Calculate the mass deficit of the helium-4 nucleus, in u.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A nuclear physicist is converting between units for a nucleus whose mass deficit is 0.0580 u. Use: 1 u = 1.66 × 10⁻²⁷ kg; c = 3.00 × 10⁸ m s⁻¹; 1 MeV = 1.60 × 10⁻¹³ J.

   (a)

   What is the mass deficit of the nucleus in kg?

   [1 mark]

   • A9.63 × 10⁻²⁹ kg
   • B9.63 × 10⁻²⁷ kg
   • C3.49 × 10²⁵ kg
   • D2.86 × 10⁻²⁶ kg

   (b)

   Which expression gives the energy equivalent, in joules, of a mass deficit Δm in kilograms?

   [1 mark]

   • AΔm c
   • B½ Δm c²
   • CΔm c²
   • DΔm / c²

   (c)

   Calculate the binding energy of the nucleus in MeV.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The binding energy per nucleon of the nuclei rises steeply from about 1 MeV for hydrogen-2 to about 7 MeV for helium-4, reaches a maximum of about 8.8 MeV near iron-56, and then falls slowly to about 7.6 MeV for uranium-235. A uranium-235 nucleus can absorb a neutron and split into two fragments of medium mass, each with a binding energy per nucleon of about 8.5 MeV.

   (a)

   Explain, with reference to the binding energy per nucleon curve, why energy is released when two light nuclei such as hydrogen-2 undergo fusion to form helium-4.

   [3 marks]

   (b)

   Use the curve to explain why fission of uranium-235 releases energy, and why fusing iron-56 with another nucleus would not release energy.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a proposed fusion reactor, deuterium and tritium nuclei fuse: ²H + ³H → ⁴He + n. Atomic masses: ²H = 2.014102 u; ³H = 3.016049 u; ⁴He = 4.002603 u; neutron = 1.008665 u. Use 1 u = 1.66 × 10⁻²⁷ kg and c = 3.00 × 10⁸ m s⁻¹. The plasma in the reactor is designed to run at about 1 × 10⁸ K, whereas the core of the Sun, where hydrogen fuses, is at about 1.5 × 10⁷ K.

   (a)

   Calculate the energy released in one fusion reaction, in J, and the energy released per kilogram of deuterium and tritium fuel used.

   [6 marks]

   (b)

   Explain why fusion requires very high temperatures and very high densities, and suggest why the reactor plasma needs to be hotter than the core of the Sun.

   [6 marks]

   Total for question 4: 12 marks

End of questions