PHYS 212 Final, Spring 1997

AUB . PHYSICS 212 : June_13, 1997 Physics Department FINAL EXAM Time 214 NB. Write your name and 1D number _on the top of your bugktet, 1)- 20 points An observer S is standing on a platform of length D, = 65m ona space station. A rocket R passes at a speed v = 0.80c moving parallel to the edge of the platform. The observer S notes that the front and back of the rocket simultaneously line up with the ends of the platform at a particular instant (fig. A) Db. +> According to S, what is the time necessary for the rocket to pass a particular point on the platform? What is the rest length L, of the rocket? According to an observer S’ on the rocket, what is the length D of the platform? According to S’, how long does it take for observer S to pass the cntire Jength of the rocket ? According to S, the ends of the rocket simultaneously line up with the ends of the platform . Are these events simultaneous to 8’? 2)- 20 points A certain accelerator produces a beam of neutral kaons ( msc” = 498 MeV ) with kinetic energy 325 MeV. Consider a kaon that decays in flight into two pions (mc? 140 MeV). Find the kinetic energy of each pion in the special case in which the pions travel parallel or antiparallel to the direction of the kaon beam. 3)- 20 points The discovery of the antiproten jf took place in 1956 at Berkeley through the following reaction: p+p—->ptp+p+ # ,in which accelerated protons were incident on a target of protons at rest in the laboratory. When the product particles in the laboratory frame S move together as if they were a single unit, find a) the magnitude v’ of the velocity of cither reacting proton in the center-of- masse reference frame S’, b) the velocity v of the incident protons in the laboratory frame. 4)- 20 points What is the wavelength of the least energetic photon in the Balmer speclruin? What is the wavelength of the series limit for the Balmer series? R-1,097x 10% m? 20 points x Tays with 2. =100 pm are scattered from a carbon target. ‘The scattered radiation is viewed at 90° to the incident beam. a) What is the Compton shift Aa ? b) What Kinetic energy is imparted to the recoiling electron? 6)- 15 points a) For n=4, what is the largest allowed value of ( ? b) What is the magnitude of the corresponding angular momentum ? ¢) How many different components on the z axis may this angular momentum vector have? d) What is the magnitude of the largest projected component ? e) What is the smallest angle that the angular momentum vector can make with the 7-aNXis? 7)- 30 points The wave function lor the ground state of the hydrogen atom is given by wr) = rye Ma, in which a) 18 the Bohr radius. za; a) Show that the ih iacnd that an electron lies within a sphere of tadius r is given by: P=1-e% (1425 +29 ), tinwhich x ~ ray. b) Evaluate the arobetility that the electron, in the ground state, will he found between the spheres r =a, and r= 2a». 8)- 15 points The nuclide °Sn (Z = 50) has a filled proton shell, 50 being one of the magic nucteon numbers. The nuclide ''Sb (Z= 51) has an extra proton outside this shell. According to the shell concept, this extra proton should be easier or harder fo remove than a proton from the filled shell. (fu =931.5 MeV ) Nuclide Z. N Atonic Mass(u) "Sb 120.003821 206 y1QT9NI1OO aaa ‘ 148.908R19 9)- 30 points The © baryonhas S=-3. K* and K® have S$ 1.=° and = have $~ -2. 4 While © ,2° 25 .A° all have S =-1. All non sirange particles such as pn, pions and 1,1)” have S= 0. Each baryon is assigned a barven number Bo +f. a) It is desired to produce the © using a beam of K” incident on protons. What other patticles are produced in this reaction? ( Use the three conservation faws for B.S and Q ). b) How might the Q decay ? ( knowing that the product particles can be A". E? Kk and 1 ). 10)- 10 points Analyze this process in terms of its quark content (u, d. ands). Yeni n Use data given in problem number 8 with the following table: . _ Baryon number 2/3 “1/3 -1/3 +1/3