Nuclear binding energyEdexcel A-Level Physics: Subtopic test

1. 1
   A student is studying the nucleus of a helium-4 atom, which contains two protons and two neutrons held together by the strong nuclear force. She is comparing the mass of the nucleus with the masses of the particles that it is made from.

   (a)

   What is meant by the mass deficit of a nucleus?

   [1 mark]

   • AThe mass of the nucleus minus the total mass of its separate nucleons
   • BThe total mass of the electrons removed from the atom
   • CThe mass of the neutrons minus the mass of the protons
   • DThe total mass of the separate nucleons minus the mass of the nucleus

   (b)

   What is the binding energy of the helium-4 nucleus?

   [1 mark]

   • AThe energy released when the nucleus decays
   • BThe kinetic energy of the nucleons inside the nucleus
   • CThe minimum energy needed to separate the nucleus into its individual nucleons
   • DThe energy needed to remove one electron from the atom

   (c)

   Explain why the mass of the helium-4 nucleus is less than the total mass of two separate protons and two separate neutrons.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The deuteron, the nucleus of hydrogen-2, contains one proton and one neutron. Nuclear mass of the deuteron = 2.013553 u. Mass of a proton = 1.007276 u. Mass of a neutron = 1.008665 u. Take $1\text{ u} = 1.661 \times 10^{-27}$ kg, $c = 3.00 \times 10^{8}$ m s⁻¹ and $e = 1.60 \times 10^{-19}$ C, so that $1\text{ MeV} = 1.60 \times 10^{-13}$ J.

   (a)

   What is the mass deficit of the deuteron in kg?

   [1 mark]

   • A$3.97 \times 10^{-27}$ kg
   • B$3.97 \times 10^{-30}$ kg
   • C$2.39 \times 10^{-3}$ kg
   • D$1.66 \times 10^{-27}$ kg

   (b)

   What is the binding energy of the deuteron in joules?

   [1 mark]

   • A$1.19 \times 10^{-21}$ J
   • B$3.97 \times 10^{-30}$ J
   • C$3.57 \times 10^{-12}$ J
   • D$3.57 \times 10^{-13}$ J

   (c)

   Use your answer to (b) to calculate the binding energy per nucleon of the deuteron, in MeV.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The Sun transfers energy to space at a rate (power) of $3.8 \times 10^{26}$ W, and this energy comes from nuclear reactions in which mass is converted to energy. The mass of the Sun is $2.0 \times 10^{30}$ kg, its age is $4.6 \times 10^{9}$ years and 1 year = $3.16 \times 10^{7}$ s. Take $c = 3.00 \times 10^{8}$ m s⁻¹ and assume that the power has been constant.

   (a)

   Calculate the mass that the Sun converts to energy each second.

   [3 marks]

   (b)

   Calculate the fraction of the Sun's present mass that has been converted to energy over its lifetime.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Data for a helium-4 nucleus: nuclear mass = 4.001506 u. Mass of a proton = 1.007276 u. Mass of a neutron = 1.008665 u. Take $1\text{ u} = 1.661 \times 10^{-27}$ kg, $c = 3.00 \times 10^{8}$ m s⁻¹ and $1\text{ MeV} = 1.60 \times 10^{-13}$ J.

   (a)

   Calculate the binding energy of the helium-4 nucleus in MeV, and its binding energy per nucleon.

   [6 marks]

   (b)

   A student states: "When protons and neutrons join to form a helium-4 nucleus, mass is destroyed, so the conservation of mass is wrong." Evaluate this statement, using the helium-4 data.

   [6 marks]

   Total for question 4: 12 marks

End of questions