Physics 102 Notes b

Physics 102 Notes b - OM D41 1.C P - PR EME Physics 102...

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Unformatted text preview: OM D41 1.C P - PR EME Physics 102 FORM 0 - PR EME D41 1.C OM [l] In a single-slit diffraction experiment, a beam of monochromatic light passes through a slit of width 16.0 fj,m. If the second dark fringe of the resulting diffraction p attern is at an angle of 4.31°, what is the wavelength of the light? [A] 301 nm [B] 413 nm (W)601 nm [D] 720 nm [E] 827 nm - PR EME D41 1.C OM - PR EME D41 1.C OM [2] A spy satellite is in orbit at a distance of 5.0 X 105 m above the ground. It carries a telescope t hat can resolve the two rails of a railroad track that are 1.4 m apart using light of wavelength 600 nm. Which one of the following statements best describes the diameter of the lens in the telescope? ^ [A] It is less than 0.26 m. QBj;It is greater than 0.26 m. [C] It is less than 0.52 m. [D] It is greater than 0.52 m. [E] It is less t han 1.4 m. - PR EME D4 11. COM [3] What is the slit spacing of a diffraction grating necessary for a 600 nm light to have a first-order principal maximum at 25.0°? U])1.42 fim [B] 2.01 /zm [C] 3.12 /xm [D] 4.12 pm [E] 5.44 fan. - PR EME D4 11. COM [4] A spaceship, traveling at O .lOOc away from a stationary enemy station, shoots a projectile towards the station with a speed of 0.560c relative to the spaceship. What is the speed of the projectile relative to the s tation? [A] 0.460c (JBj)0.487c [C] 0.492c [D] 0.625c [E] 0.660c - PR EM ED4 11. COM [5] A satellite, initially at rest in deep space, separates into two pieces which move away from each other. One-piece has a rest mass of 190 kg and moves away with a speed of 0.280c, and the second piece moves in the opposite direction with a speed of 0.600c. What is the rest mass of the second piece? __ [A] 42.4 kg [B] 52.7 kg [C] 68.8 kg (13)73.9 kg [E] 88.7 kg - PR EM ED4 11. COM [6] A space tow barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the tow barge have to do to accomplish this? [A] 8.78 x 1019 J [B] 1.35 x 1020 J (fcfo.OS x 1020 J [D] 2.70 x 1020 J ^-^ 11. COM [E] 5.42 x 1020 J - PR EM ED4 [7] If you approximate yourself as a blackbody emitter and you don't have a fever, what is the peak f requency of your emission? [B] 5.8 x 1012 Hz [C] 6.3 x 1012 Hz [D] 9.7 x 1012 Hz ED4 11. COM 2.2 x 1012 Hz 1013 Hz 11. COM - PR EM [8] An x-ray photon with an energy of 1.00 X 10~15 J travels in the +x direction and is incident on a free electron that is at rest at the origin. The photon is scattered in the — y direction. What is the f requency of the scattered photon? ~^ 17 17 17 [A] 1.49 x 10 Hz [B] 1.50 x 10 Hz [C] 1.51 x 10 Hz nD])l.49 x 1018 Hz PRE MED 411 .CO MPRE M ED4 11. COM - PR EM ED4 [E] 1.51 x 1018 Hz OM D41 1.C P - PR EME Physics 102 FORM 0 1.C OM - PR EME D41 1.C OM [9] A large collection of non-relativistic electrons has a mean kinetic energy of 1.0 eV w ith a corresponding spread/uncertainty in their momenta of 10%. What is the corresponding minimum spread/uncertainty in their positions? (OlxlO™9m [B] 5 x 10~9 m [C] 1 x 10~8 m [D] 3 x 10~8 m 7 Ej 2 X 1 0~ m PRE MED 411 .CO MPRE M ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EME D4 11. COM - PR EME D4 11. COM - PR EME D41 1.C OM - PR EME D41 [10] The line emission in the excited gases that you observed through the d iffraction gratings during class is due to the excited constituent atoms decaying back to their ground state. The lifetime of these transitions is typically 10~7 seconds. Use the Heisenberg Uncertainty Principle to compute the corresponding minimum spread/uncertainty in the energy of the excited state. This spread in energy gives rise to the finite width of the emission line. JAJ 5 X 10~28 eV [B] 1 x 10~27 eV [C] 3 x 10~27 eV [D] 1 x 10~9 eV 9 (tip X 10- eV OM D41 1.C P - PR EME Physics 102 t'l - PR EME D4 11. COM - PR EME D41 1.C OM - PR EME D41 1.C OM - PR EME D41 1.C OM [11] Two glass plates (in air) are separated by parallel fine wires, separated by a distance of 7.50 cm, as shown. The first wire, at x = 0, has a diameter ^ = 0.0400 m m, and the second wire, at x = 7.50 cm, has a diameter d2 = 0.0415 mm. Monochromatic light of wavelength A = 600 nm is incident from above. (a) Consider interference between light reflected from the b ottom surface of the upper plate and light reflected from the top surface of the lower plate, and find an expression for the values of the separation t between these surfaces for which the interference is destructive. (b) Find an expression for the values of x for which the interference is destructive. (c) What is the horizontal distance (thus along the z-axis) between adjacent dark bands in the reflected light? x [cm] 7.50 - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EME D4 11. COM o.oo PRE MED 411 .CO MPRE M ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM (c) 2. - 0( OM D41 1.C P - PR EME hysics 102 OM 1.C D41 - PR EME OM 1.C COM - PR EME D41 (Albert^ 411 .CO MPRE M ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EME D4 11. COM - PR EME D4 11. H (IV) MED \^\ ^^ [t>) - PR EME D41 1.C OM [12] Max and Albert are identical twins. On their 18t!l birthday, Albert takes off on an O utward Bound spaceship expedition traveling in the z-direction at a speed of 4c/5 with respect to Earth. Max stays on Earth and attends the University of Miami. A fter 3.0 years on Albert's watch/calendar, Albert's Outward Bound spaceship reverses direction and heads back to Earth on the same path at a speed of 4c/5. (a) What is the age difference between Albert and Max once Albert returns to Earth (who is older)? (b) In Albert's frame of reference, his spaceship is 100 m long as measured along the xdirection. How long does Max measure the spaceship to be in the z-direction? (c) According to Max, what f raction.of the spaceship's total relativistic energy (during its travel) is relativistic kinetic energy? PRE £3) FORM 1 OM D41 1.C P - PR EME Physics 102 FORM 0 COM - PR EME D4 11. COM - PR EME D41 1.C OM - PR EME D41 1.C OM - PR EME D41 1.C OM [13] A gamma ray photon of energy E propagates in the +x direction and collides with an identical gamma ray photon (also of energy E) traveling in the — x direction. Since parts (b) and (c) depend on your answer for part ( a), it is suggested that you express your answers for parts (b) and (c) in terms of E, before evaluating numerical results. This way appropriate credit could be given on p arts (b) and (c) even if your answer for part (a) is wrong. (a) What is the minimum energy of each of these photons such t hat they produce a positronelectron pair? (Hint: the minimum energy results in a positron and an electron that are at rest.) (b) An x-ray with 1/100,000 the energy of the above gamma ray is incident on a gold surface with a work f unction of 4.58 eV. What is the the maximum kinetic energy (in eV) of the ejected photoelectron? (c) What is the de Broglie wavelength (in m eters) of the ejected electron t hat has the maximum kinetic energy found in part ( b)? (Hint: the ejected electron is NOT moving at relativistic speeds, and be careful w ith units! It is suggested to express the electron energy and mass, in the formula you use, either in Joule and kg u nits, or in eV and eV/c2 units.) - PR EM ED4 11. COM - PR EME D4 11. Use- - MJ PRE MED 411 .CO MPRE M ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM - PR EM ED4 11. COM / 00,000 - few /°°?00 OM D41 1.C P FORM 0 - PR EME Physics 102 - PR EME D41 1.C OM FORMULAE SHEET me = 9.11 x 10~31^ = 0.511MeF/c2, OM e = 1.60 x lO"19^ D41 e0 = — - PR EME L r2 ' go' ' 2e0' e0 ' ^-* e0 4eo fcg , - PR EME D41 1.C C/jg = 8.85 x lQ-l2C2/Nm2 4?TK OM r2 lkWh = 3.Q x 106J, 1.C leV = 1.60 x 10~19 J, k = 8.99 x WgNm2/C2 lir = ^-, E = cB, COM k E = E0sin(kx -uJt), - PR EME D4 o» Ap I J0 c jr> / '"i » -^vac / \« — T? — — . J a0 ' «0 Ti n d sin^ = (m + 1 /2)A, m = 0 , l , 2 . . . (double slit, dark) - PR EM —— COM \f = c (resolution) r ^' SI Tt I L - PR EM ED4 11. (single slit, d ark) = 3.00 X 108rra/.s, _ 11. COM j 1 c= ED4 GO ,2..., (double slit, grating, bright) ' F 11. U j - PR EME D4 —-— , Z_i Z 11. COM H, ,-7 r ™ a n = 4?r X 10 —— » COM (thin film, L= L n \ / l — U ^ / C ^ , q - PR EM p £- ' O — , A/1 - t ) 2 /C 2 JT P P K = E - E0, D= P2 E =p2 0+pc, E , 22 11. COM = "i0c2 , -. c •Ua,. = -— . 2 ED4 11. , - PR EM ED4 = 6.626 x 10~S4J s = 4.135 x 10~15eF s = 1 2 4 0 , H = — = 1.054 x 1 0~ 34 J s c 2?r = 5.88 x lO10*"1^1, ^max = hf - W0 , ^ = hf MED 411 .CO MPRE M ED4 11. COM ~, 2m PRE A ' - A = A c (l-cos0), ED4 hf = hf' + K, - PR EM p= — = -, c A 11. COM - 2.898 x 1 0" 3 m-^, , s -, 2 > 2 AC = - = 2 .426pm, m ec m A dB = - . T - 273.15 K = Tc = (Tp - 3 2°) . . c '•'•' '; ...
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