A neutron is absorbed by a nucleus of uranium-235 ( 235
1. [1 mark] 92U). One possible
outcome is the production of two nuclides, barium-144( 144
56Ba) and krypton-89
( 89 36Kr).
How many neutrons are released in this reaction?
A. 0 B. 1 C. 2 D. 3
2. The mass of a nucleus of iron-56 (56Fe) is M. [1 mark]
26 What is the mass defect of the nucleus of iron-56?
A. M − 26m p − 56m n B. 26 m p + 30m n − M C. M − 26m p − 56m n − 26m e D. 26m p + 30m n + 26m e − M
3. What is the relation between the value of the unified atomic mass unit in [1 mark] grams and the value of Avogadro’s constant in mol−1? A. Their ratio is 1. B. Their product is 1. C. Their sum is 1. D. Their difference is 0. 4. In a hydrogen atom, the sum of the masses of a proton and of an electron [1 mark] is larger than the mass of the atom. Which interaction is mainly responsible for this difference? A. Electromagnetic B. Strong nuclear C. Weak nuclear D. Gravitational
5. During the nuclear fission of nucleus X into nucleus Y and nucleus Z, [1 mark] energy is released. The binding energies per nucleon of X, Y and Z are BX , BY and BZ respectively. What is true about the binding energy per nucleon of X, Y and Z?
A. BY > BX and BZ > BX
B. BX = BY and BX = BZ C. BX > BY and BX > BZ D. BX = BY + BZ
6. The mass of nuclear fuel in a nuclear reactor decreases at the rate of [1 mark] 8 mg every hour. The overall reaction process has an efficiency of 50 %. What is the maximum power output of the reactor? A. 100 MW B. 200 MW C. 100 GW D. 200 GW
7. Which property of a nuclide does not change as a result of beta decay? [1 mark] A. Nucleon number B. Neutron number C. Proton number D. Charge
3 8. The rest mass of the helium isotope 3 He is m . [1 mark] 2 Which expression gives the binding energy per nucleon for 32He ? (2mp+mn+m)c2 A. 3 (2mp+mn−m)c2 B. 3 C. (2m p + mn + m)c2 D. (2 mp + mn − m)c2
9. The positions of stable nuclei are plotted by neutron number n and proton [1 mark] number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β-) particles? 10. The graph shows the variation of the number of neutrons N with the [1 mark] atomic number Z for stable nuclei. The same scale is used in the N and Z axes.
Which information can be inferred from the graph?
I. For stable nuclei with high Z, N is larger than Z. II. For stable nuclei with small Z, N = Z. III. All stable nuclei have more neutrons than protons.
A. I and II only B. I and III only C. II and III only D. I, II and III
11. The average binding energy per nucleon of the 15 O nucleus is 7.5 MeV. [1 mark] 8 What is the total energy required to separate the nucleons of one nucleus of 15 8 O? A. 53 MeV B. 60 MeV C. 113 MeV D. 173 MeV
12. A graph of the variation of average binding energy per nucleon with [1 mark] nucleon number has a maximum. What is indicated by the region around the maximum? A. The position below which radioactive decay cannot occur B. The region in which fission is most likely to occur C. The position where the most stable nuclides are found D. The region in which fusion is most likely to occur 13. What gives the total change in nuclear mass and the change in nuclear [1 mark] binding energy as a result of a nuclear fusion reaction?
14. What is the definition of the unified atomic mass unit? [1 mark] 1 A. 12 the mass of a neutral atom of carbon-12 B. The mass of a neutral atom of hydrogen-1 1 C. 12 the mass of a nucleus of carbon-12 D. The mass of a nucleus of hydrogen-1
15. In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a [1 mark] nucleus of element Y and a nucleus of element Z. X + n → Y + Z + 2n magnitude of the binding energy per nucleon of Y total binding energy of Y and Z What is and ? magnitude of the binding energy per nucleon of X total binding energy of X
16. What is the energy equivalent to the mass of one proton? [1 mark] A. 9.38 × (3 × 108)2 × 106 J B. 9.38 × (3 × 108)2 × 1.6 × 10–19 J 9.38×108 C. J 1.6×10−19 D. 9.38 × 10 8 × 1.6 × 10–19 J
11 17. The binding energy per nucleon of 11 Be is 6 MeV. What is the energy [1 mark] 4 required to separate the nucleons of this nucleus? A. 24 MeV B. 42 MeV C. 66 MeV D. 90 MeV
18. In the nuclear reaction X + Y → Z + W, involving nuclides X, Y, Z and W, [1 mark]
energy is released. Which is correct about the masses (M) and the binding energies (BE) of the nuclides?
19. When an alpha particle collides with a nucleus of nitrogen-14 (14 N), a [1 mark] 7 nucleus X can be produced together with a proton. What is X? A. 18 8 X
B. 17 8 X C. 18 9 X D. 17 9 X
20. The mass defect for deuterium is 4×10 –30 kg. What is the binding energy [1 mark] of deuterium? A. 4×10–7 eV B. 8×10–2 eV C. 2×106 eV D. 2×1012 eV
21a. State what is meant by the binding energy of a nucleus. [1 mark]
21b. Draw, on the axes, a graph to show the variation with nucleon number [2 marks] A of the binding energy per nucleon, BE A . Numbers are not required on the vertical axis.
21c. Identify, with a cross, on the graph in (a)(ii), the region of greatest [1 mark] stability.
21d. Some unstable nuclei have many more neutrons than protons. Suggest [1 mark] the likely decay for these nuclei.
Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).
The following data are available for binding energies per nucleon: plutonium 7.568 MeV uranium 7.600 MeV alpha particle 7.074 MeV
21e. Show that the energy released in this decay is about 6 MeV. [3 marks]
21f. The plutonium nucleus is at rest when it decays. [2 marks]
kinetic energy of alpha particle Calculate the ratio . kinetic energy of uranium
The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10−10 s−1.
21g. Estimate the power, in kW, that is available from the plutonium at [3 marks] launch.
8 21h. The spacecraft will take 7.2 years (2.3 × 108 s) to reach a planet in the [2 marks] solar system. Estimate the power available to the spacecraft when it gets to the planet.
Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.
21i. State and explain what happens to the kinetic energy of an emitted [2 marks] photoelectron.
21j. State and explain what happens to the rate at which charge leaves the [2 marks] metallic surface.
Radioactive uranium-238 ( 238
92U) produces a series of decays ending with a stable nuclide of lead. The nuclides in the series decay by either alpha (α) or beta-minus (β−) processes.
22a. Uranium-238 decays into a nuclide of thorium-234 (Th). [1 mark]
Write down the complete equation for this radioactive decay.
22c. The half-life of uranium-238 is about 4.5 × 109 years. The half-life of [4 marks] thallium-206 is about 4.2 minutes. Compare and contrast the methods to measure these half-lives. The graph shows the variation with the nucleon number A of the binding energy per nucleon.
22d. Outline why high temperatures are required for fusion to occur. [2 marks]
22e. Outline, with reference to the graph, why energy is released both in [1 mark] fusion and in fission.
22f. Uranium-235 ( 235 92U) is used as a nuclear fuel. The fission of uranium- [2 marks]
235 can produce krypton-89 and barium-144.
Determine, in MeV and using the graph, the energy released by this fission.
One possible fission reaction of uranium-235 (U-235) is
140 235U + 1n 92 0 → 54Xe + 94 1 38Sr + 2 0n Mass of one atom of U-235 = 235 u Binding energy per nucleon for U-235 = 7. 59 MeV Binding energy per nucleon for Xe-140 = 8. 29 MeV Binding energy per nucleon for Sr-94 = 8. 59 MeV
23a. State what is meant by binding energy of a nucleus. [1 mark]
23b. Outline why quantities such as atomic mass and nuclear binding energy [1 mark] are often expressed in non-SI units.
23c. Show that the energy released in the reaction is about 180 MeV. [1 mark]
A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to 180 MeV of energy.
23d. Estimate, in J kg−1 , the specific energy of U-235. [2 marks]
23e. The power station has a useful power output of 1. 2 GW and an [2 marks] efficiency of 36 %. Determine the mass of U-235 that undergoes fission in one day.
23f. The specific energy of fossil fuel is typically 30 MJ kg –1 . Suggest, with [1 mark] reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.
A sample of waste produced by the reactor contains 1. 0 kg of strontium-94 (Sr-
94). Sr-94 is radioactive and undergoes beta-minus (β − ) decay into a daughter nuclide X. The reaction for this decay is 94 38Sr → X + v̄e + e.
23g. Write down the proton number of nuclide X. [1 mark]
The graph shows the variation with time of the mass of Sr-94 remaining in the sample.
23h. State the half-life of Sr-94. [1 mark]
23i. Calculate the mass of Sr-94 remaining in the sample after 10 minutes. [2 marks]
24a. Radioactive decay is said to be “random” and “spontaneous”. Outline [2 marks]
what is meant by each of these terms. Random: Spontaneous:
A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234.
The following data are available. Energy released in decay 4.27 MeV Binding energy per nucleon for helium 7.07 MeV Binding energy per nucleon for thorium 7.60 MeV
24b. Calculate the binding energy per nucleon for uranium-238. [3 marks]
24c. Calculate the ratio kinetic energy of alpha particle [2 marks]
. kinetic energy of thorium nucleus
2 Deuterium, 21 H, undergoes fusion according to the following reaction. 2H + 2H → 31 H + X 1 1
25a. Identify particle X. [1 mark]
The following data are available for binding energies per nucleon. 2H = 1.12MeV 1 3H = 2.78MeV 1
25b. Determine, in MeV, the energy released. [2 marks]
25c. Suggest why, for the fusion reaction above to take place, the [2 marks] temperature of deuterium must be very high.
Particle Y is produced in the collision of a proton with a K- in the following
reaction.
The quark content of some of the particles involved are
25d. Identify, for particle Y, the charge. [1 mark]
25e. Identify, for particle Y, the strangeness. [1 mark]
26a. Rutherford constructed a model of the atom based on the results of the [2 marks] alpha particle scattering experiment. Describe this model.
Rhodium-106 (106 106
45 Rh) decays into palladium-106 ( 46 Pd) by beta minus (β ) –
decay. The binding energy per nucleon of rhodium is 8.521 MeV and that of palladium is 8.550 MeV.
26b. State what is meant by the binding energy of a nucleus. [1 mark]
26c. Show that the energy released in the β– decay of rhodium is about 3 [1 mark] MeV. β– decay is described by the following incomplete Feynman diagram.
26d. Draw a labelled arrow to complete the Feynman diagram. [1 mark]
