PHYS 212 Final, Fall 1996

ae Per AREY Lith aAk poo teers | a 3 A.U.B. Physics 212 Jan. 29 ,1997 Physics Department Final Exam Time 2 Hours gei to wre yo 0 ¢ And LL.D). + On the £0) All supplementary information is given at the end of your exam sheet Part I- Relativity 4)-15 Marks A particle at rest with mass M decays into two particles of equal mass m. calculate the speed of the two decay particles. Give numerical answer for the decay of a rho particle (M, = 770 MeV/c’ ) into two charged pions (m,= 40 MeV/c’ ). 2)- 15 Marks Two protons are directed toward each other. As measured in the laboratory frame, the protons have speed |Vi| = | ¥2| = 0.85 c. What is the speed of one proton in the rest frame of the other? 3)- 15 Marks Calculate the speed of a galaxy relative to the Earth if the red shift causes the photon wavelength to bee doubled. 4)- 25 Marks Two protons each with energy of 500 GeV , travel in the opposite direction and collide. Calculate the energy ofeaeof the protons in the frame where the other proton is at rest. Part H- Quantum physics §)- 15 Marks a)- What should the energy of the photons be so that the maximum change in wavelength due to Compton scattering by electrons is one percent? b)- Using these photons, what is AA in A for Compton scattered photons at 60° from the incident beam? c)- What is the energy of the recoil electron in this case? 6)- 15 Marks It is possible for a muon p to be captured by a proton to form a muonic atom. The muon mass is 105.5 MeV/c”. a)- Calculate the radius of the first Bohr orbit of a muonic atom ( taking into account the reduced mass effect ). b)- Caleulate the magnitude of the lowest energy. c)- What is the shortest wavelength in the Lyman series for this atom? 7)- 15 Marks Consider a system of two electrons, each with @ =1, and s=%. a)- Neglecting spin, what are the possible values of the quantum number for the total orbital angular momentum L = L; +1? b)- What are the possible values of the quantum number S for the total spin $=8,+8, c)- Using the results of parts a) and b), find the possible quantum numbers j for the combination J=L +8. d)- What are the possible numbers j; and jz for the total angular momentum of each particle? e)- Use the result of part d) to calculate the possible values of j from the combination of j; and jz . Are these the same as in part c) ? 8)- 15 Marks Which of the following transitions in Sodium do not occur as_ electric dipole transition? Give the selection rule that is violated. The levels are written in the spectroscopic notation: n[symbol of 2]; - 48 38, - 4D 3P a) y > Ss y d) ¥ > 3Py -4 - 4 3P b) Sy > 3P;, e) D,, > 3Py c} 4Ps, > 38 f)- 4D, > 38y 9)- 20 Marks r . . 1 1 4% The wavefunction of the Hydrogen ground stateis ‘Y,,, = = ~3z7 & ™ va a; a)- What is the radial probability density to find the electron anywhere in the spherical shell of radius r and thickness dr? b)-Calculate the probability that the electron in the ground state of Hydrogen will be found outside the first Bohr radius a,. You may use the integration by parts : 6 {ua = wh - frau a Part II- Nuclear and Elementary Physics 10)- 15 Marks Calculate the decay rate per gram per min,of a living organism, assuming the ratio 4c = 13 x 107, and ty2("C) = 5730 years. 11)- 25 Marks A person works for 4 hours in a room that contains an unshielded 10 mCi Co source. Knowing that Co —> Ni (stable) +e (~ 1MeV) +X. The angular distribution of the emitted electrons is isotropic. a)-Identify the particle X. b)- What is the activity of the source . ( 1Ci = 3.7 x 10°Bq) c)-What is the total energy that appears in electrons in 4 hours. d)- If all of this energy were absorbed by a person of mass 60 kg, what is the radiation absorbed dose in Gray (Gy) and in Sievert (Sv)? (1 Gy = 6.24 x 10” MeV/kg). e)- The maximal recommended occupational dose is 50 mSv per year. To get one- hundredth of this dose what is the fraction of the electrons absorbed? f)- If the area of the person is 0.5 m’ , at what distance the person must keep from the source, to limit the dose to 0.5 mSv ? 12)- 10 Marks In the quark model, the nucleon {p,n} and the two A- particles {A‘, A° } are represented by the same combinations : { wud, udd }. Even that, these two sets of particles are different. What is the main difference between them? Given: Re =h/me = 0.0243A, iInm=10A ,m,=0.511 MeWc”, m, = 938.28 MeWc? In = nF /mke? = 0.53 va A, vj/c=a/n, E,=- mc” o2/2n’, he= 1240 eV.nm, ke?=1.44eV.nm , x = lew inev)y=s4. ’ ju 133 ,