Hjälpmedel: Physics Handbook samt räknedosa. Tabell över vissa kärndata bifogas.

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1 Tentamensskrivning i Kärnfysik (FK7010), 7,5hp Fredag den 28 mars 2008 kl 9-15 Hjälpmedel: Physics Handbook samt räknedosa. Tabell över vissa kärndata bifogas. Denna tentamen består av två delar. Den första delen består av 13 flervalsfrågor där ett eller flera svarsalternativ är korrekta. Ange vilka genom att skriva ner svarsalternativet/en på ett av de papper du lämnar in ( t.ex 4d+e). Varje rätt svar ger 1p. Felaktiga svar ger avdrag så att om alla 5 alternativ skull angivits på en fråga summan blir 0p. Den andra delen omfattar frågorna För dessa problem skall fullständiga lösningar lämnas in. Glöm inte att ange de antaganden och approximationer du gör. Motivera varje steg i lösningen. Även om du inte i detalj kan slutföra en lösning kan en god beskrivning av principerna för lösningen ge poäng. En helt korrekt lösning ger 4p. För godkänt krävs minst 6p på var del och 16p totalt. Lycka till. /ChrB Means: Physics Handbook and calculator. Table of certain nuclear data is enclosed. This exam comprises two parts. The first part contains 13 multiple choice questions with one or more correct answers. Write down the correct answer(s) on a paper that you hand in (e.g. 4d+e). Every correct answer gives 1p. Incorrect answers render deductions such that if all 5 alternatives would be given as an answer to one question the sum would be 0p. The second part comprises problems Here complete solutions should be handed in. Do not forget to clearly state your assumptions and approximations. Explain every step of the solution clearly. Even if you are not able to complete a solution in all detail a good account of the principles for a solution can render points. A completely correct solution is worth 4p. A passing grade requires at least 6p on each part and 16p in total. Good luck! /ChrB

2 1. How large is the Q-value of the alpha decay of 210 Po? 1a) 5.4 MeV 1b) 5.9 MeV 1c) 6.4 MeV 1d) 6.9 MeV 1e) 7.4 MeV 2. How large is the Q-value of the β + -decay of 22 Na? 2a) 1.82 MeV 2b) 2.03 MeV 2c) 2.33 MeV 2d) 2.57 MeV 2e) 2.84 MeV Cd with a half-life of 49 minutes decays to the ground state of 118 In that has a halflife of 5 seconds and decays to 118 Sn. Starting with a 1 GBq source of pure 118 Cd approximately how many decays per second of 118 In occur after 1 hour and 38 minutes? 3a) 0 3b) c) d) e) There are two stable isotopes of copper, 63 Cu and 65 Cu with a natural abundance of 69.1 and 30.9 percent respectively. The thermal neutron cross section of 63 Cu and 65 Cu is 4.5 b and 2.17 b respectively and the half-life 12.7 h and 5.10 m. A foil of natural copper is inserted into a thermal neutron flux of neutrons s -1 m -2. When it is extracted after one week the 64 Cu activity is 20 MBq. What is the activity of 66 Cu? 4a) 4.3 MBq 4b) 8.9 MBq 4c) 93 MBq 4d) 1.3 GBq 4e) 3.0 GBq 5. In the decay of a deformed nucleus one observes three gamma transitions. Is it likely that the energies of the three transitions are approximately: 5a) 90, 210 and 330 kev? 5b) 500, 550 and 1050 kev? 5c) 540, 550 and 560 kev? 5d) 90, 300 and 630 kev? 5e) 90, 95 and 100 kev?

3 6. In an even-even nucleus an excited state with spin 4 and positive parity decays directly to the ground state emitting a gamma-ray. What multipolarities of the gamma-ray are possible? 6a) E2 6b) M2 6c) E3 6d) M4 6e) E4 7. In an electron capture decay 7a) the emitted neutrinos are mono-energetic 7b) the neutrinos are emitted with energies ranging between 0 and the Q-value of the decay. 7c) no neutrinos are emitted 7d) no electrons are emitted 7e) the emitted electrons are mono-energetic. 8. Approximately how high is the Coulomb barrier in case of alpha-decay of 210 Po. 8a) 5 MeV 8b) 15 MeV 8c) 25 MeV 8d) 50 MeV 8e) 200 MeV 9. A light ion moving through matter at an energy of a few MeV per nucleon looses energy. The energy loss per unit path length depends 9a) linearly on the density of electrons in the matter 9b) inversely on the density of electrons in the matter 9c) increases with increasing velocity 9d) decreases with increasing velocity 9e) is independent of the charge of the particle. 10. What is the effective dose to a patient if during a treatment the thyroid receives a gamma ray dose of 2 Gy? The weighting factor for the thyroid is a) 0.1 Gy 10b) 0.1 Sv 10c) 2 Sv 10d) 40 Gy 10e) 40 Sv

4 11. During a diagnostic X-ray, a broken leg with a mass of 5 kg receives an equivalent dose of 0.4 msv. If the X-ray energy is 50 kev, how many X-ray photons were absorbed? 11a) b) c) d) e) At a Rutherford backscattering analysis you use 10 MeV alpha particles on a thick and homogenous silicon sample containing traces of arsenic and cadmium. Which of the following is true? 12a) In the energy spectrum of alpha particles there appear narrow peaks corresponding to scattering on arsenic and cadmium. 12b) There is a sharp fall-off of the count rate in the spectrum above 8.7 MeV. 12c) There is essentially no count rate in the spectrum below 5.5 MeV. 12d) There is a continuous background in the spectrum due to protons from alpha-particle break up. 12e) There is a greater sensitivity for cadmium than for arsenic. 13. A natural uranium, thermal fission reactor is operating at a thermal power output of 3 GW. What is the total rate of consumption of 235 U per second? Take the energy release per fission to be 200 MeV. The thermal fission and capture cross sections of 235 U are σ f = 579 b and σ C = 101 b respectively. 13a) 27 mg 13b) 32 mg 13c) 37 mg 13d) 43 mg 13e) 51 mg

5 14. In the single-particle shell model, the ground state of a nucleus with an odd proton and an odd neutron is determined from the coupling of the proton and neutron shell model states: I = j p + j n. Consider the following nuclei with their ground state spin and parity: 16 N (2 - ); 12 B (1 + ); 34 P (1 + ); 28 Al (3 + ). Draw simple vector diagrams illustrating these couplings, then replace j p and j n, respectively, by l p + s p and l n + s n. Examine your four diagrams and deduce an empirical rule for the relative orientation of s p and s n in the ground state. Finally, use your empirical rule to predict the ground state spin and parity, I π, assignments of 26 Na and 28 Na. 15. The radioactive isotope 15 O, which has important medical applications can be produced in the reaction 12 C(α,n). a) The cross section reaches a peak when the laboratory energy of the incident alpha particles is 14.6 MeV. What is the excitation energy of the compound nuclear state? b) The reaction cross section at the above incident energy is 25 mb. Assuming a carbon target of 0.10 mg/cm 2 and a current of 20 na of alpha particles, compute the 15 O activity that results after 4.0 minutes of irradiation. 16. If all the neutrons produced in a D-T reactor were slowed and absorbed in a natural lithium medium a) what is the thermal energy that would be produced per incident neutron? b) How many tritium atoms would be produced per incident thermal neutron? For thermal neutrons the cross sections are: 38.5 mb for the reaction 6 Li(n,γ) 7 Li, 940 b for the reaction 6 Li(n,α) 3 H and 45.4 mb for the reaction 7 Li(n,γ) 8 Be. 17.Support your answers with facts from the table: a) Why is germanium considered to be a better material than silicon for detection of gamma rays? b) Estimate the energy resolution (in kev) of a germanium detector for 1 MeV gamma rays.

6 17 c) The figure shows a spectrum recorded with a germanium detector irradiated by 2 MeV gamma rays. Explain the occurrence of the four indicated structures. A A D C B

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