Hjälpmedel: Physics Handbook. Kopior ur läroboken bifogas, räknedosa finns att tillgå vid tentamen.

Transcription

1 Tentamensskrivning i Kärnfysik (FK7010), 7,5hp Torsdagen den 15 mars 2012 kl Hjälpmedel: Physics Handbook. Kopior ur läroboken bifogas, räknedosa finns att tillgå vid tentamen. Denna tentamen består av två delar. Den första delen består av 12 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). Helt rätt på en fråga ger 1p. Felaktiga svar ger avdrag så att om alla 5 alternativ skulle ha angivits på en fråga blir summan 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 betyg krävs minst 6p på var del. Lycka till. /Per-Erik T. Means: Physics Handbook. Copies from the textbook are enclosed, calculator can be borrowed at the exam. This exam comprises two parts. The first part contains 12 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 correctly answered question 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. Good luck! /Per-Erik T.

2 1. According to the independent particle shell model what is the expected spin and parity of the first excited state of 207 Pb? The shell model level scheme is given below. a) 1/2 - b) 3/2 - c) 5/2 - d) 7/2 - e) 9/2 -

3 2. Which of the following statements about β decay processes is/are correct? a) The mass number A of the parent and daughter nucleus differs by one unit. b) In a β - decay a neutron is converted into a proton. c) In an electron capture decay a proton is converted into a neutron. d) In a β - decay the emitted electron is monoenergetic. e) In an electron capture decay the emitted neutrino is monoenergetic. 3. Which of the following statements about fusion reactors is/are correct? a) The most promising fusion reaction is p+p. b) The most promising fusion reaction is d+d. c) The most promising fusion reaction is d+t. d) The fusion cross section for d+t is larger than that for d+d (at the same energy). e) In the most promising fusion reaction the plasma is heated with emitted γ rays. 4. Which of the following statements about positron emission tomography (PET) is/are correct? a) Compounds labeled with β - (beta-minus) active isotopes are injected into the body. b) The technique is based on coincident detections of two 511 kev γ rays. c) The technique is based on coincident detections of electron-positron pairs. d) PET can be used to map different activities of the brain. e) PET gives information on the distribution of hydrogen in the brain. 5. Fifty per cent of cells in a piece of tissue survive after being irradiated with 10 equal dose fractions, given at intervals sufficiently far apart in time for cell recovery to take place. Calculate the surviving fraction if the total dose were given in a single exposure. Assume a model for cell survival in which the cell must receive two or more damaging hits before the cell is killed and thus (using Poisson statistics) the probability for cell survival is given by the probability for at most one damaging hit, i.e. P ( 0) + P )1(1( = + µ ) e µ where µ, the expected average number of damaging hits, is proportional to the dose. The surviving fraction will be approximately a) 0.88 b) 0.68 c) 0.48 d) 0.28 e) 0.08

4 6. I 1 I 2 The sketch is a schematic representation of a piece of bone surrounded by tissue irradiated with 60 kev gamma rays. If the ratio of transmitted γ-ray intensities I 1 (through tissue) to I 2 (through tissue-plus-bone) is 2, calculate the thickness of the bone given that the mass attenuation coefficients (for 60 kev γ-rays) of tissue and bone are 0.20 and 0.32 cm 2 g -1 and the densities 1.0 and 1.8 g cm -3 respectively. a) 0.8 cm b) 1.3 cm c) 1.8 cm d) 2,3 cm e) 2.8 cm 7. If a natural uranium, thermal fission reactor is operated at a thermal output level of 3 GW, what is the approximate rate of production of 239 Pu due to thermal-neutron capture, assuming that all neutrons captured by 238 U lead to 239 Pu. Take the energy release per fission to be 200 MeV, σ f (235)=579b and σ c (238)=2.72 b. a) 0.76 kg y -1 b) 7.6 kg y -1 c) 76 kg y -1 d) 760 kg y -1 e) 7600 kg y The flux of electromagnetic radiation reaching the Earth from the Sun above the atmosphere (solar constant) is 1.4 kw m -2. Approximately how large is the flux of neutrinos from the Sun? a) m -2 s -1 b) m -2 s -1 c) m -2 s -1 d) m -2 s -1 e) m -2 s Use the semi-empirical mass formula to estimate what is the lightest even-even nucleus with Z=4 n and A=8 n that can (theoretically) undergo symmetric fission and where n is an integer. [You find values for the parameters of the semi-empirical mass formula in Physics Handbook.] a) 56 Ni b) 72 Kr c) 80 Zr d) 88 Ru e) 96 Cd

5 10. What is the energy of the alpha particles emitted in the decay of the ground state of 212 Rn to the ground state of 208 Po? a) 6.26 MeV b) 6.38 MeV c) 6.50 MeV d) 6.62 MeV e) 6.74 MeV 11. Which of the following statements concerning a fast (fission) breeder reactor is/are true? a) It is a strong source of neutrinos. b) It is a strong source of antineutrinos. c) Graphite may be used as a moderator. d) The spent fuel is strongly radioactive. e) It produces more (potential) fuel than it consumes. 12. A 5 g sample of natural silver is put in a flux of thermal neutrons, 10 7 m -2 s -1. What is the number of 107 Ag nuclei transformed (to 108 Ag) in 1 minute? The thermal neutron capture cross section of 107 Ag is 37 b. a) 530 b) c) d) e)

6 13. The nucleus 87 Rb decays into the ground state of 87 Sr, with a half-life of years and a maximum β-energy of 272 kev. a) Discuss briefly the difficulties you might encounter in attempting to measure this halflife. b) Five different samples of meteorites are found to have the following proportions of 87 Rb, 87 Sr and 86 Sr. Meteorites 87 Rb/ 86 Sr 87 Sr/ 86 Sr Modoc Homestead Bruderheim Kyushu Bath Furnace Given that the nucleus 86 Sr is not a daughter product of any long-lived radioactive nucleus, show that these data are consistent with a common primordial ratio 87 Sr/ 86 Sr and a common age for all these meteorites and find that age. 14. The β - -decay of a certain nuclear ground state has two components, with maximum energies and MeV. The first component is coincident with two γ rays: and MeV, that are also coincident with each other. The second component is coincident with γ rays of 0.604, 0.308, 0.136, 0.468, 0.612, 0.296, and MeV. (Some of these γ rays may or may not be coincident among them selves.) a) Use this information to construct a decay scheme [the level scheme of the daughter nucleus showing which levels are populated in the β decay and between which levels the various γ transitions occur, and the excitation energy of each level]. b) Find the nuclear mass difference between the nuclear ground states. 15. By irradiating uranium by thermal neutrons the following reaction is possible: U+ 0n 57 La+ 35Br + x 0n, where x is the number of emitted neutrons. a) Determine the value of x. b) How much energy is liberated in this reaction? (The mass excess of 148 La is µu). c) 148 La is not stable and decays in several steps to the stable nucleus 148 Nd. Which is the decay mode and how much energy is liberated in this process?

7 16. An thin aluminum foil is bombarded with a 10 na beam of 5 MeV α particles in a Rutherford back scattering (RBS) experiment, to determine the level of cadmium contamination. The α particles scattered in an angle 180 are detected in a detector, which subtends a solid angle of steradians. The energy spectrum of α particles corresponding to scattering from cadmium in the foil is shown below Counts E E 0 a) Calculate the maximum energy E 0. b) What determines the energy spread E (which is considerably greater than the detector resolution)? c) After 10 minutes 30 counts corresponding to scattering from cadmium are recorded in the detector. Calculate the level of cadmium contamination (mass per unit area). The scattering differential cross section is given by the Rutherford scattering formula in Physics Handbook. E

8

9

10

11

12

13

14

15

16

17

18

19 I I ~_Z;ov - I~ ~.~,~,, ~~ :~ ~ -~ ~ ~ I ~ ~ hj -; ~ I I ~ --::.~--. -_ ~---- ~ I i~f~f~ ~ :. ;~ : -, ~i ~I ~~~zz_ ~:~zzz_ I ~_!~L~_~_

20 ~-o~--. cj~-~--~ fl) -~ ~~ 5-~J~ ~ ~ ~ ~. -~ ---~ c~ -.~ ~ I -~ ~ c_-.~_~ ~ ~ ~.- - _[~ ----~N~ r-~ ~ _~Z~~i~ I ~ -s ~ ~ ~~~ _i~ez~ee~e~ez~$ ~ ~ ~ ~ ~~ - F~ L~ ~ zz~ -~~- H---S~-j-~ ~ ~ -~ ~ l~r~- ~_~r ~ ~ ~-øç~ ~ : ~ ~. ~, -~ ~m ~ :~: r----~-- -: z~t ~ ---~-----~ : I ~

21 I I I ~ - I I I b I~ t~ w i r~ ~ c ~ : -ç -~ ~,%~ -:~i~~ ~.sj~..i~z~ ~ ~ h~ -~--_-~-:-----_-_- ~ --~L ~ H-~r~ ~ ~ ~l ~ - I N~-~ ; -~ U ~ I I L. ~ I I : H- -. ~- $ -~.~-- -~~. ~~ t~- --~ I I ~ c~ - ~ ~ \~% ~ ~ -----~-. ~----H ~I I I~I U_ I i-- - ~ ~ ~ ~ ~ ~%L_. ZE:m ~ z~zrz±z~ Th~ ~ II

22 V V.~,) I V L ~ ~ r - V~ ~ ~ rr~ ~ I 9 ~ V -~_ ~ ~ - ~ VI - -~ ~%4~) ~ --~~ - ~r F I ~z~zz~ z~zz~z. ~- ~ -\~--V -- fl ft ~-_---~~, -~ ~ ~ ~ -._ ~7~~ V - -. ; ---- L~_~V V I i~-- -~ ~.z- ~ ~ V - 4 ~ V. -- ~ s ~J. V ~ I : V -_ ~ ~ I V V V ç ~ ~t ~ --- I. ~~ I V : V V ~ V V -~ ~ -~----~--~ : ~ V

23

24 I L r~qz~~- ~- -~_ L. 1.. ~ I ~ :,( rr~~ I~.~~ ç ~Li ~ ~ ~~-,~-----~ ~_i ~ ~, ~- ---~ ~%_N.M~ ~ ~ ~* ~ _ ~ Li rzzthe~_~~ee~_h ~-- ~~ ~- -f~ --~ -~ ~-~--~ ~ I ~ ~:.t~ I I~ * I LC~ LL~ ~

25 ~ - I~ II, II - ~ ~- ~ ~ i~ ~~i ~_ -~ I ~ c.~--~ H JtlZi Ii ~- I~I ---~C - ~ 1r4.. *~--~_~;_~ ~ -~: 4 ~cs~ ]%i%~~~ f ~ ~,- --- s-- 4 r L_~ L~.~ ~ ~ ~-- ~- ~ ~ ~ ~SE~% Z~~L -~ %%~~ L t~% I ti\,, \ -~\ I f ~ze~z~t~ ~zz:~zzzz~z~..- ~\\N\~_.~- ~ ~ ~-4--- lit I t% ~ I ~ C- L iz J, - - I I r ~ I ~ ~.~ ii f ~ j L ~ I. -