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# solutionsfinal - SOLUTIONS"Physics 273— Final Exam...

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Unformatted text preview: SOLUTIONS "Physics 273— Final Exam Wednesday, December 21, 2011 Prof. Mohan Kalelkar Your name sticker with exam code . The exam will last from 9:55am to 11:00am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information now, before the exam starts. . In the section labelled NAME, enter your last name, then ﬁll in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. . Under STUDENT # enter your 9—digit Student ID Number. Under COURSE enter 273.. Under CODE enter the exam code given above. . During the exam, you may use pencils, a calculator, and ONE 8%” x 11” sheet of paper with formulas and notes. . There are 16 multiple—choice questions on the exam. For each ques- tion, mark only one answer on the answer sheet. There is no subtrac— tion of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in only the answer sheet. Retain this question paper for future reference and study. . Useful numerical constants are given on the next two pages. Before starting the exam, make sure that your copy contains the pages of constants and all 16 questions. Bring your exam to the proctor if this is not the case. ' Elementary charge 8 = 1.6 X 10'19 C 1 electron volt (6V) = 1.6 X 10“19 J Speed of light 0 = 3 X 108 m/s Planck’s constant h = 6.63 X 10—34 J - s = 1240 nm - eV/c h = h/ 271' ' Avogadro’s number = 6.02 X 1023 molecules/mole Electron mass = 9.11 X 10’31 kg = 0.511 Mel/702 = 0.000549 u Proton mass = 1.673 X 10'27 kg = 938.3 MeV/02 Neutron mass = 1.675 X 10’27 kg = 939.6 Mel/702 = 1.008665 u Hydrogen atom mass = 1.007825. u Atomic mass unit 1 u. = 931.5 M elf/02 Fine structure constant a = 1/137 Hubble constant H = 0.0215 m/s/lz'ght year = 70 km/s/Mpc 1 parsec (pc) = 3.26 light years . Powers of ten: femto(f) pico(p) nano n) micro(u) milli(m) 10“15 10‘12 10“9 10—6 10—3 centi(c) kilo(k) Mega(M) Giga(G) Tera(T) 10’2 10+3 10+6 10+9 10+” THE LEPTONS (all spin Mass (MeV) Common decays LE L), L Antiparticle e“ (.511) Stable 1 0 0 8+ 1/.3 (0?) Stable 1 0 0 We if (106) €7,911), 0 1 0 ,u+ 1/), (0?) Stable 0 1 0 Z, T“ (1777) 7r“7roz/T, (fizz/T, ,u’ﬁMI/T 0 0 1 7+ 1/7 (0?) Stable 0 . 0 1 7T THE QUARKS (all spin Baryon number = +1 / 3 for all quarks, and —1/3 for all antiquarks S = strangeness, C = charm, B = bottomness, T = topness Name Symbol Charge S C B T Antiparticle Down d —1/3 0 0 0 0 3 Up u +2/3 0 0 0 0 a Strange 5 —1/3 —1 0 0 0 E Charm 0 +2 / 3 0 +1 0 0 5 Bottom 17 — 1/3 0 0 — 1 0 5 Top t +2 / 3 0 0 0 +1 if HADRONS (strongly interacting particles) Baryon number = +1 for baryons, —1 for antibaryons, 0 for all others S = strangeness, C = charm, B = bottomness ' SOME BARYONS (all are fermions: half—integer spin) Mass (MeV) Common decays S C B Antiparticle p (938) Stable O O O p n (940) 19678 O O 0 ﬂ A (1116) 1971‘, 71710 —1 O 0 A 2+ (1139) m0, mr+ —1 0 0 '2“ 2° (1193) A) —1 0 0 ‘2‘” 2* (1197) m- —1 0 0 2+, 30 (1315 A710 —2 0 0 E” a" (1321) A71“ —2 0. 0 T 12— (1672) AK“, 5%“ —3 0 0 D“ A: (2285) Various 0 +1 0 Kc— A; (5624) Various 0 0 —1 71‘; SOME MESONS (all are bosons: integer spin) Mass (MeV) Common decays S C B Antiparticle 71+ (140) ‘ ,LL‘l'z/ﬂ 0 O 0 7T— 710 (135) 7')! O O 0 Self 770 (547) 27, 3710,... O . O 0 Self K+ (494) ,LL‘l'Vl), 7r+7ro +1 0 0 K— K0 (498) 271, 33,... +1 0 0 76° D+(1869) Ki+...,K°+... 0 +1 0 D“ D0 (1865) Ki+...,K°+... 0 +1 0 ‘D‘0 D: (1969) Ki+...,K°+... +1 +1 0 D; J/¢ (3097) Various 0 - O 0 Self 13+ (5279) Di+...,D°+... 0 0 +1 B- 30(5279) Di+...,D°+... 0 0 +1 “E” T (9460) Various 0 0 0 Self 23 ~; (wt, 4'an wry!ch 1. What is the average binding energy per nucleon for \$30, whose atomic mass is 13.003355 u? (See the page of constants for other relevant masses). ' ) 7.23M6V 5::— (6YWWW)+(7XI, Medan/3.0193355" a «a b 7.47M V 2.9073245 ’ V c) 7.71 MZV 7: (Jaw; wc'bX‘isA 5' m%’s2) ~ ‘37, NW ) d) 64.8MeV . ) 787MeV g d 477.)! x 7’47 mel/ e r- A )3 '2. Which of the following statements about the strong nuclear force is false? -—~? a) It causes radioactivity to occur. K FWK 56 b) It is much stronger than the gravitational force between two nucleons separated by about 1 fm. c) It is much stronger than the electrical force between two nucleons I separated by about 1 fm. d) It is charge-independent. e) It is short—range. 3. What is the ratio of the nuclear volume of 3371313 to that of \$1149? )About6.8 Rwﬂv“ pavd «3%,4 a b) About 1.0 v N? c) About 8.6 .7 (:1) About 1.9 Jig .- 25: 2. 6 e) About 2.1 4’ W2 4. For a certain radioactive substance, it is found that 25% of the nuclei decay (D in 3.0 hours. What is the half—life of the substance? M 96\$, a) About 12 hours ‘ 25‘ N 5-. Na -- N ,e y“? b) About 7.2 hours :1: 0 W C) About 0.75 hours 5? we" .5 .75 Q w“/\ :11 3 45)» (:1) About 1.5 hours ) About 6.0 hours > A 5. J 095‘? ﬁx") ‘5) ﬁnal ,1, 7 «W 5. Which of the following statements is false? a) When a nucleus undergoes ,6+ decay, the charge of the nucleus de— creases. b) When a nucleus undergoes ,6“ decay, a neutron in the nucleus turns into a proton. % c) When a nucleus undergoes ﬂ“ decay, the Q—value (decay energy) is negative. d) When a nucleus undergoes 3+ decay, the Q—value (decay energy) is positive. e) When a nucleus undergoes 7 decay, the charge of the nucleus remains unchanged. 6. The 14C isotope is radioactive with a decay constant A = 1.21 X 10"4 yr“? All living organisms have an activity of 0.255 decays/ second per gram of carbon. If a certain dead organism is found to have an activity of 0.060 decays/ second per gram of carbon, how long ago did it die? “M a) Between 1000 and 10000 years ago Alva: . Oé 0 ‘5 AM? ’5 “ xi b) Less than 10 years ago :5 i 759' .2. «.7 c) More than 10000 years ago ' f; v, >4; d) Between 10 and 100_years ago Q a '23; *3 6 , e) Between 100 and 1000 years ago 7e. _, :2 A? 1709 W. . =9 “ “1.2 2‘ 7. Consider the nuclear reaction 3He+.1,4N —>§7 O+§H. The atomic masses are M(He) = 4.002603 11, M(N) = 14.003074 u, M(O) = 16.999133 u, = 1.007825 11. What is Q, the net kinetic energy released, and what conclusion can be drawn from the sign of Q? a) Q = +1.19 M eV, so some kinetic energy was converted to mass b) Q = +1.19 M 6V, so some mass was converted to kinetic energy c) Q i —1.19 M 6V, so the reaction can’t occur a d) Q = —1.19 M 6V, so some kinetic energy was converted to mass e) Q = —1.19 M 6V, so some mass was converted to kinetic energy a = (4. 002603—1- 14.1w 3074/16, “717/ 33a], 00721259693}..59 ~ .... j, I? Nev In 8. Which of the following statements are true? 0 I: The sun releases energy because hydrogen nuclei are undergoing fusion. 0 II: Stars whose mass is much smaller than that of our sun will even- tually turn into neutron stars or black holes. 0 III: When 235U undergoes ﬁssion into 1443a and 89K7", energy is re leased because U has more binding energy per nucleon than do Ba andKr. \Lesg III is true; I and II are not I and II are true; III is not All three statements are false I and III are true; II is not I is true; II and III are not a b c d VVVVV My CD 9. Only one of the following reactions or decays CANNOT occur. Which is it? For the reactions, assume that the projectile always has enough energy for the reaction to occur, if other applicable conservation laws permit). ~98) Vu+p~>n+u+ (ram; [2“ ) 7r‘+p->n+7r° )r+p~n+ﬁ ) p+p~p+p+p+n ) ,uf.—>e“+y#+ve b c d e 10. Which of the following statements is false? a) In any reaction, the number of baryons (minus anti~baryons) is Con- served. -«—§ b) Inlany reaction, the number of mesons (minus anti~mesons) is con- served. c) In any reaction, the number of leptons (minus anti-leptons) is con~ served. d) Anti-baryons are composed of three anti~quarks. e) Mesons are composed of one quark and one anti~quark. 11. An electrically neutral particle has strangeness ~1, charm O, and bottom- ness +1. Which of the following is a possible quark composition for this particle? a 5 C B a) 55 0 at 0 «H W b) 5g 0 +1 0 «- l c) us? 0 “I 0 “‘ I d) tab 0 +1 0 +1 e) 5573 l o +) 4 + J 12. Consider the hypothetical strong interaction process B++E‘ —> Aﬁ—i—DS‘ + D”. Which conservation laws does it satisfy, and which does it violate? Conserves strangeness, but neither charm nor bottomness 397.14" N695 ' a) b) Conserves charm and bottomness, but not strangeness +1H~3 é a l +19 ’5“ 0 c) Conserves strangeness and bottomness, but not charm a d) Conserves strangeness and charm, but not bottomness e) Conserves bottomness, but neither strangeness nor charm 13. A photon strikes a stationary proton, causing the following reaction to occur: 7 + p —> A + K+. What is the minimum energy E that the photon must have if this reaction is to occur? a) E<650MeV Q=o+qsgwmgﬂ47¢~s «672 WV b) 650, s E < 750MeV 9 If c) 750 g E < 850MeV » (“‘72) M Q d) 850__<_ E<950MeV K73, ~ "‘ ' (3X63 9) e) E 2 950MeV :1— a) 3 Mal’. 14. According to the General Theory of Relativity, which of the following state- ments are true? ' o I: The effects of acceleration and gravitation cannot be distinguished in a closed laboratory. 0 II: To an external observer, a black hole contracts forever towards its Schwarzschild radius, but never quite gets there. 0 III: The path of light is unaffected by gravity. ) All three statements are true ) I and II are true; III is false ) I and III are true; II is false ) I is true; II and III are false ) III is true; I and II are false 15. The Lyman alpha line of hydrogen has a wavelength of 122 nm in the labo— ratory. For a certain galaxy, the same line is measured to have a wavelength of 300 nm. How far away is the galaxy? A A ~ ‘ 39.9 H. ' 2 LP 5 a) About 2.0 x 109 light years 3:0 F 122 P I; (3 r I b About 4.0 x .109 light years HE ) . ,... I c) About 6.0 x 109 light years “'39 lag ’7 é ’ ps- =i> @ ’ ' 7/; 01) About 8.0 x 109 light years 8) ‘ 2 7,, w 5 About 1.0 x 1010 light years R , 3.): :3 ’W 7,. [,ﬂ g/p f H ., 0215 Am’S/fg‘ 16. An antiproton of kinetic energy 1200 M eV moves to the right. A proton of kinetic energy 400 M eV moves to the left. The two collide head—on, producing the reaction 3—) + p —;> 7r° + X. What is. the maximum mass of X that can be produced in this way? ' a) About 3341 M eV/c2 b) About 2762 M eV/ 62 c) About 3476 M eV/ c2 d) About 1819 M eV/c2 ~w§ e) About 3204 M eV/ 62 “A? / a. 2 ’ W4 Emu» Mﬂpc +Mxé #WMX 5F ‘ 432—!“1200 : 2132 MY} AV ET“. :- ¢= 733+ 41812 ’1 E . , v i: \lCﬂIEBDQ" (4397’ 2 'z +1471: “2/3" / .4754:- Mel/a l3: 7, a (Barf/[73'3" c _‘ V A: r19 : [421’45lr7 447 m/c' T 2 ‘ ' 2,. 1 4:; 333‘! WV. Ecm- ‘ ETH- ”‘ {ST ‘3' c (3476') (4‘47) ' L £504: 7;: 6cm Q 4 {VI/gag:- + Mxﬁl ’7 + MXC ﬂ QC' :3; an‘z a 340+mav‘ ...
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