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23.1. Mass defect and nuclear binding energy
A subsection of Physics, 9702, through 23. Nuclear physics
Listing 10 of 52 questions
In some power stations, nuclear fission is used as a source of energy. State what is meant by nuclear fission. The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10. Complete the nuclear equation for the absorption of a single neutron by a boron-10 nucleus with the emission of an a-particle. 5B + 3Li + Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction.
9702_w10_qp_41
THEORY
2010
Paper 4, Variant 1
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In some power stations, nuclear fission is used as a source of energy. State what is meant by nuclear fission. The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10. Complete the nuclear equation for the absorption of a single neutron by a boron-10 nucleus with the emission of an a-particle. 5B + 3Li + Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction.
9702_w10_qp_42
THEORY
2010
Paper 4, Variant 2
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State the basic assumptions of the kinetic theory of gases. Use equations for the pressure of an ideal gas to deduce that the average translational kinetic energy of a molecule of an ideal gas is given by the expression = T where R is the molar gas constant, NA is the Avogadro constant and T is the thermodynamic temperature of the gas. A deuterium nucleus 2 1H and a proton collide. A nuclear reaction occurs, represented by the equation 1H + 1 1p 2He + c. State and explain whether the reaction represents nuclear fission or nuclear fusion. R NA For the reaction to occur, the minimum total kinetic energy of the deuterium nucleus and the proton is 2.4 × 10–14 J. Assuming that a sample of a mixture of deuterium nuclei and protons behaves as an ideal gas, calculate the temperature of the sample for this reaction to occur. temperature = K Suggest why the assumption made in may not be valid.
9702_w10_qp_43
THEORY
2010
Paper 4, Variant 3
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State what is meant by nuclear fusion and nuclear fission. nuclear fusion: nuclear fission: A nuclear reaction which may, in the future, be used for the generation of electrical energy is H H + He x + . Name the particle x. Data for the binding energy per nucleon EB of some nuclei are given in . binding energy per nucleon EB / 10–13 J deuterium H tritium H helium He 1.7813 4.5285 11.3290 1. State the binding energy per nucleon of x. binding energy per nucleon = J 2. Calculate the energy change that takes place in this reaction. energy change = J Use your answer in part 2 to determine the energy release when 2.0 g of deuterium ( H 2 ) reacts with 3.0 g of tritium ( H 3 ). energy = J To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series.
9702_w18_qp_42
THEORY
2018
Paper 4, Variant 2
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One possible nuclear reaction that takes place is 2U + 1 0n 2Mo + 13 7La + 21 0n + 7–1 0e Data for nuclei in this reaction are given in . nucleus mass / u total mass of separate nucleons / u mass defect / u binding energy per nucleon / MeV 2Mo 7La 2U 94.906 138.906 235.044 95.765 140.125 236.909 0.859 1.219 1.865 8.443 8.189 Show that the energy equivalent to a mass of 1.00 u is 934 MeV. Use data from to calculate the binding energy per nucleon of a nucleus of uranium-235 (23 2U). Complete . The nucleon number of an isotope of the element rutherfordium is 267. State whether the binding energy per nucleon of this isotope will be greater than, equal to or less than the binding energy per nucleon of uranium-235. Calculate the total energy, in MeV, released in this nuclear reaction. energy = MeV The nuclei in 1.2 × 10–7 mol of uranium-235 all undergo this reaction in a time of 25 ms. Calculate the average power release during the time of 25 ms. power = W
9702_w19_qp_41
THEORY
2019
Paper 4, Variant 1
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One possible nuclear reaction that takes place is 2U + 1 0n 2Mo + 13 7La + 21 0n + 7–1 0e Data for nuclei in this reaction are given in . nucleus mass / u total mass of separate nucleons / u mass defect / u binding energy per nucleon / MeV 2Mo 7La 2U 94.906 138.906 235.044 95.765 140.125 236.909 0.859 1.219 1.865 8.443 8.189 Show that the energy equivalent to a mass of 1.00 u is 934 MeV. Use data from to calculate the binding energy per nucleon of a nucleus of uranium-235 (23 2U). Complete . The nucleon number of an isotope of the element rutherfordium is 267. State whether the binding energy per nucleon of this isotope will be greater than, equal to or less than the binding energy per nucleon of uranium-235. Calculate the total energy, in MeV, released in this nuclear reaction. energy = MeV The nuclei in 1.2 × 10–7 mol of uranium-235 all undergo this reaction in a time of 25 ms. Calculate the average power release during the time of 25 ms. power = W
9702_w19_qp_43
THEORY
2019
Paper 4, Variant 3
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Two vertical metal plates are separated by a distance d in a vacuum, as shown in . plate Y plate X nucleus with charge +q path d +V (not to scale) The potential difference (p.d.) between the plates is V. A nucleus with charge +q is initially at rest on plate X. The nucleus is accelerated by the uniform electric field from plate X along a horizontal path to plate Y. State expressions, in terms of some or all of d, q and V, for: the magnitude of the electric field strength electric field strength = the magnitude of the electric force acting on the nucleus force = the kinetic energy of the nucleus when it reaches plate Y. kinetic energy = State the change, if any, in the kinetic energy of the nucleus on reaching plate Y when the following separate changes are made. The distance d is halved, but the p.d. V remains the same. The nucleus is replaced by a different nucleus that is an isotope of the original nucleus with fewer neutrons. The nucleus is carbon-14 (14 6C). This nucleus decays to form a new nucleus by releasing a β– particle and only one other particle of negligible mass. Calculate the nucleon number and the proton number of the new nucleus. nucleon number = proton number = State the name of the particle of negligible mass.
9702_w20_qp_23
THEORY
2020
Paper 2, Variant 3
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State what is meant by nuclear fusion. On , sketch the variation of binding energy per nucleon with nucleon number A for values of A between 1 and 250. binding energy per nucleon A On your line in , label: a point X that could represent a nucleus that undergoes alpha-decay a point Y that could represent a nucleus that undergoes nuclear fusion. A nucleus Z undergoes nuclear fission to form strontium-93 ( 93 38Sr) and xenon-139 (139 54Xe) according to 0n + Z 38Sr + 139 54Xe + 21 0n. Table 9.1 shows the binding energies of the strontium-93 and xenon-139 nuclei. Table 9.1 nucleus binding energy / J 38Sr 1.25 × 10–10 54Xe 1.81 × 10–10 The fission of 1.00 mol of Z releases 1.77 × 1013 J of energy. Determine the binding energy per nucleon, in MeV, of Z. binding energy per nucleon = MeV
9702_w23_qp_41
THEORY
2023
Paper 4, Variant 1
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State what is meant by nuclear fusion. On , sketch the variation of binding energy per nucleon with nucleon number A for values of A between 1 and 250. binding energy per nucleon A On your line in , label: a point X that could represent a nucleus that undergoes alpha-decay a point Y that could represent a nucleus that undergoes nuclear fusion. A nucleus Z undergoes nuclear fission to form strontium-93 ( 93 38Sr) and xenon-139 (139 54Xe) according to 0n + Z 38Sr + 139 54Xe + 21 0n. Table 9.1 shows the binding energies of the strontium-93 and xenon-139 nuclei. Table 9.1 nucleus binding energy / J 38Sr 1.25 × 10–10 54Xe 1.81 × 10–10 The fission of 1.00 mol of Z releases 1.77 × 1013 J of energy. Determine the binding energy per nucleon, in MeV, of Z. binding energy per nucleon = MeV
9702_w23_qp_43
THEORY
2023
Paper 4, Variant 3
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Questions Discovered
52