Foundations of Physics II

Intro Elec and Wave Motion

Modern Physics II

Exam-PHYS1004-2008April.pdf-PHYS 1004 April 2008 Exam Questions

w Carleton t, .6 I l UNIVERSITY =xa$f1ffiror,r APRIL, 2OO5 DURATION: 3 HOURS No. of Students: 16 Department Name & Course Number: PHYS 3606 A Courselnstructor(s) B.J. Jarosz AUTHORIZED IIEUORANOA Letter size original hand written aid sheet and calculator Students MUST count the number of pages in this examination question paPer before beginning to write, and report any discrepancy to a proctor. This question paper has 3 pages. This examination question paper may be be taken from the examination room. ln addition to this question paper, students require: an examination booklet yesE noE a Scantron sheet yesfl noB I nstruction to students Write your name and student number on the examination booklet. Write the solutions of PartI and ll in the examination booklet. Answer eachproblem on a separate page of the examination booklet.Only first two solutions of part ll will be marked. lf you attempted morethan two problems of part ll and you prefer the solutions at the back marked, cross outthe solutions notfor marking. PHYSICAL CONSTANTS Electronic charge, Electronic mass, Speed of light in vacuum, Planck's constant, Usefulintegral:1 -r ) < xe = 'Jrr e = 1.60 x 1O-1s C rn = 9.11 x 10-31 kg c = 3 x 108 m/s h = 6.63 x 1O-s J s. 1 L PFIYS 3606Final examinatron April 18.2005 Part l. Answer all questions. 1 Consider electrons rn a periodic crystalline lattice. a) Showthat the electron wavefunction musthave exponential form to satisfy periodicity condition ; b) Prove thatthe setof equations in nearly-free electron approximation model _ h-k- (E, - .-lan-Vrar=g 2m .2 n v,ao -tE; - ;rE * 2n6,)'lo, = o leads to discontinuity in electron's energy. 2. The constants in semiempirical formulafor nucleus bindingenergy ar€&y61 = 15.75 MeV; osurf = 17.8 MeV; oCoul = 0.711MeV; &sym = 23.7MeY:.and spair = ll.2 MeV. (a) What do the constants represent in termsof the nucleus binding-energy model? (b) Find the moststable isotope amongst A = 125isobars; (c) Use the attached fragmentof the periodictableto identify the isotope. 3. An crparticle is accelerated in a cyclotron with a magnetic field of 1.2 T and a maximumorbitalradius of 80 cm. (a) Find the maximum momentum the particlecan acquire; (b) What should be the frequency of the accelerating voltage? 4. A 20-keV photon scatters on a free electron through 1350. (a) Find the shift in its wavelength; (b) What percent shift in wavelength was this? Partll. SolveANYTWOproblems. 5. In a lattice,concentration of electrons in the energyinterval E, E + dE is given by o 6* 6'tt2 O\ Ltu '\t1, t) n\b)df-= n, m;- ru an e kur +r Find concentration of conduction electrons in an ir"itrinsic semiconductor around room temperature. Assumeforbiddenenergygap to be AE. HINT: Around room temperature ks T << E - Er . i 6. A parent nucleus with l,r decay constant decays into,,a radioactive daughter nucleus of decayconstant 1.2.Suppose the numberof parent nuclei is Nro at time t = 0 and the numberof daughter nuclei is zero at that time. (a) Find the numberof daughter nuclei as a function of time; (b)The half-life of 218Po p-"nt nucleus is 3.11 min, while its daugh^ter nucleus 2laPb decays with a half-life of 26.8min. At what time is the numberof ""Pb maximum? 7. A nucleus X p decays into a nucleus Y. In a special case, with X exactly at rest the electron happens to be also exactly at rest. ') 7 t

PHYS | 3606 | Modern Physics II | exam | w Carleton t  .6 I l UNIVERSIT

\"--' cI'"'\ DURATION: 3 HOURS No. of Students: 21 Department Name & Course Number: Course Instructor(s) B.J. Jarosz PHYS lOO2A Students MUST count the number of pages in this examination question paper before beginning to write, and report any discrepancy to a proctor. This question paper has LI pages. This examination question paper may be be taken from the examination room. In addition to this question paper. students require: an examination booklet yesi) noQ a Scantron sheet yesQ noCi Instruction to students ~ Write your name and student number on the examination booklet. Write the missing v'/ords in sentences of Part I in the examination booklet. Answer 43ach problem on a sepjarate page of the examination booklet. Only first four solutions will be marked. If you attempted more than four problems and you prefer thE3 solutions at the back marked, (~ross out the solutions not for marking. PHYSICAL CaNST ANTS e = 1.60 x 10.19 C m=9.11 X 10.31 kg c = 3 x 108 m/s Jlo = 47t X 10-7 Him h = 6.63 x 10-34 J s. Electronic charge, Electronic mass, Speed of light in vacuum, Magnetic permeability in vacuum, Planck's constant, PHYS 1002* exam. April 20, 2005 2 Part I Complete the following statements by writing the missing words in the examination booklet. Each answer is 1 mark. The light emitted by the spark is causedby of free electron and ion 2. A solid sphere of radius R has the charge Q uniformly distributed in its volume. The field at a radial distance r < R has the magnitude with r. 3, When an insulator with dielectric constant K fills a capacitor with charge on its plates constant, the p.d. betweenthe plates by a factor of K 4. The magnetic field due to a current is to the direction of the current. 5 The magnetic field outside a circular loop of wire has the pattern characteristic for a 6. The magnetic dipole moment on the atomic scale is momentum. to the angular 7. Electrons move in a wire to produce a current I because there is an metal. inside the 8. Capacitors in electriccircuits areused to rapid changes in voltage. 9. The statement that powerin a circuit is I ~ V is valid for 10.The statement that anyround-trip integralof the electricfield in a circuit mustbe zerocomes from conservation. 11.The Hall effectcan be used to determine the magnitude and direction of the field. 12.Gauss's law in electricityis valid for surface. 13. The differential form of Ampere's law involving the curl is a equation. 14. The curl of electric field is proportional to partial derivative of the magnetic field. 15. The radiation electric and magnetic fields of a point charge vary with the radial distance r as 16. In the curl of magnetic field of Ampere-Maxwell law, one of the terms is the vector.

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