PY 407 HW #2 (Sp09) (778061)
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1 1/22/09 1:08 PM PY 407 HW #2 (Sp09) (778061) Fri Jan :00 PM EST Details TR3 2.P.06. [427711] In the 1887 experiment by Michelson and Morley, the length of each arm was 11 m. The experimental limit for the fringe shift was fringes. If sodium light was used with the interferometer (! = 589 nm), what upper limit did the null experiment place on the speed of the Earth through the expected ether? 3.47 km/s 2. Details TR3 2.P.12. [427751] Determine the ratio " = v/c for each of the following. (a) A car traveling 100 km/h. 9.29e-08 (b) A commercial jet airliner traveling 300 m/s. 1.00e-06 (c) A supersonic airplane traveling mach 2.1. (Mach number = v/v sound. Assume the speed of sound is 343 m/s.) 2.41e-06 (d) The space shuttle, traveling 21,000 km/h. 1.95e-05 (e) An electron traveling 33 cm in 2 ns (f) A proton traveling across a nucleus (10-14 m) in s Details TR3 2.P.13. [427812] Two events occur in an inertial system K as follows. Event 1: x 1 = a, t 1 = 2a/c, y 1 = 0, z 1 = 0 Event 2: x 2 = 2.5a, t 2 = 1.7a/c, y 2 = 0, z 2 = 0 What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using the variables a and c and the unit vectors, i, j, and k; for example, 2*i + 2*j is a vector which bisects the x and y axes *c*i 4. Details TR3 2.P.14. [427764] An event occurs in system K' at x' = 2 m, y' = 3.7 m, z' = 3.7 m, and t' = 0. System K' and K have their axes coincident at t = t' = 0, and system K' travels along the x axis of system K with a speed 0.94c. What are the coordinates of the event in system K? x = 5.86 m 61&deployment= &UserPass=a127aaaf17bd4de17a e Page 1 of 3
2 1/22/09 1:08 PM y = z = t = 3.7 m 3.7 m 1.84e-08 s 5. Details TR3 2.P.16. [427738] Two events occur in an inertial system K as follows. Event 1: x 1 = 0.5a, t 1 = 2a/c, y 1 = 0, z 1 = 0 Event 2: x 2 = 2a, t 2 = 4.9a/c, y 2 = 0, z 2 = 0 Is there a frame K' in which the two events occur at the same place? yes no If "yes", then determine the velocity of K' relative to K. If "no", then determine the velocity of the frame in which the two events are simultaneous. Express the velocity vector using the variables a and c and the unit vectors, i, j, and k; for example, 2*i + 2*j is a vector which bisects the x and y axes *c*i 6. Details TR3 2.P.20. [427847] Astronomers discover a planet orbiting around a star similar to our sun that is 15 light years away. How fast must a rocket ship go if the round trip is to take no longer than 30 years in time for the astronauts aboard? c How long will the trip take as measured on Earth? 42.4 yr 7. Details TR3 2.P.31. [427849] A spaceship is moving at a speed ot 0.7c away from an observer at rest. A boy in the spaceship shoots a proton gun with protons having a speed of 0.8c. (a) What is the speed of the protons measured by the observer at rest when the gun is shot away from the observer? c (b) What is the speed of the protons measured by the observer at rest when the gun is shot toward the observer? c Name (AID): PY 407 HW #2 (Sp09) (778061) Locked: Yes Author: Kustusch, Mary Bridget ( mbkustus@ncsu.edu ) Last Saved: Jan 7, :24 PM EST 61&deployment= &UserPass=a127aaaf17bd4de17a e Page 2 of 3
3 1/22/09 1:08 PM PY 407 HW #3 (Sp09) (778063) Fri Jan :00 PM EST Details TR3 2.P.59 revised [ ] A particle having a speed of 0.90c has a momentum of kg!m/s. What is its rest mass? 1.61e-25 kg 2. Details TR3 2.P.66. [427719] The Tevatron accelerator at the Fermi National Accelerator Laboratory (Fermilab) outside Chicago actually consists of 5 stages to sequentially boost protons to 1 TeV (1000 GeV). What is the speed of the proton at the end of each stage? Note: the numbers given in parentheses represent the total kinetic energy at the end of each stage. Cockcroft-Walton (750 kev) 0.04 c Linac (400 MeV) c Booster (8 GeV) c Main ring or injector (150 GeV) c (express to at least 5 decimal places) Tevatron itself (1 TeV) c (express to at least 7 decimal places) 3. Details TR3 2.P.70. [427773] What is the speed of a deuteron when its kinetic energy is equal to 7 times its rest energy? c 4. Details MI2 05.X revised [ ] An alpha particle (a helium nucleus) is moving at a speed of times the speed of light. Its mass is ( kg). (a) What is its rest energy? 5.76e-10 J (b) Is it okay to calculate its kinetic energy using the formula? Yes, because the formula for kinetic energy is always correct. Yes, because. No, because this formula isn't valid for speeds near the speed of light. (c) What is its kinetic energy? 1.03e-08 J (d) Which is true for this situation? 63&deployment= &UserPass=a127aaaf17bd4de17a e Page 1 of 2
4 1/22/09 1:08 PM The kinetic energy is much smaller than the rest energy. The kinetic energy is approximately equal to the rest energy. The kinetic energy is much bigger than the rest energy. 5. Details TR3 2.P.78 revised [ ] A test automobile of mass 950 kg moving at high speed crashes into a wall. The average temperature of the car is measured to rise by 0.6 C after the wreck. What is the change in mass of the car? (Assume the average specific heat of the automobile is close to that of steel, 0.11 cal!g -1! C -1.) 2.91e-12 kg Where does this change in mass come from? Key: The source of this energy is the internal energy of the arrangement of atoms and molecules prior to the collision. Name (AID): PY 407 HW #3 (Sp09) (778063) Locked: Yes Author: Kustusch, Mary Bridget ( mbkustus@ncsu.edu ) Last Saved: Jan 21, :50 PM EST Permission: Protected Randomization: Person Which graded: Last Publish Essay Scores Help/Hints Publish Essay Scores Help/Hints Key 63&deployment= &UserPass=a127aaaf17bd4de17a e Page 2 of 2
5 3/10/09 4:08 PM PY 407 HW #7 (Sp09) (813861) Fri Mar :00 PM EDT Details TR3 5.P.42. [427707] Find the minimum uncertainty in the speed of a proton having mass 1.67e-27 kg if we know the position of the proton to within 2e-15 m, that is, to about its own size. 1.58e+07 m/s 2. Details TR3 5.P.43. [427756] An atom in an excited state of 4.9 ev emits a photon and ends up in the ground state. The lifetime of the excited state is s. (a) What is the energy uncertainty of the emitted photon? ev (b) What is the spectral line width (in wavelength) of the photon? nm 3. Details TR3 5.P.44. [427885] An electron microscope is designed to resolve objects as small as 0.10 nm. What energy electrons must be used in this instrument? 151 ev 4. Details TR3 5.P.48. [427884] The wave function of a particle in a one-dimensional box of width L is (x) = Asin(!x/L). If we know the particle must be somewhere in the box, what must be the value of A? Express your answer in terms of L. sqrt(2/l) Name (AID): PY 407 HW #7 (Sp09) (813861) Locked: Yes Author: Kustusch, Mary Bridget ( mbkustus@ncsu.edu ) Last Saved: Feb 13, :14 PM EST Permission: Protected Page 1 of 2
6 3/10/09 4:08 PM PY 407 HW #8 (Sp09) (813862) Fri Mar :00 PM EDT Details TR3 6.P.11. [427810] A wave function has the value A sin x between 0 and!, but zero elsewhere. Normalize the wave function and find the probability that the particle is between x = 0 and Details TR3 6.P.16. [427868] An electron moves with a speed v = 10-5 c inside a one-dimensional box (V = 0) of length 364 nm. The potential is infinite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have? 3 3. Details TR3 6.P.17. [427787] For the infinite square-well potential, find the probability that a particle in its seventh excited state is in each third of the onedimensional box: (0 x L/3) (L/3 x 2L/3) (2L/3 x L) 4. Details TR3 6.P.21. [440010] An electron is trapped in an infinite square-well potential of width 0.5 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.) highest 22.6 ev 18.1 ev 12 ev 10.5 ev 7.53 ev lowest 4.52 ev Name (AID): PY 407 HW #8 (Sp09) (813862) 62&deployment= &UserPass=27a9288ba2ff45f04a4b4deaaac9c66c Page 1 of 2
7 4/6/09 5:42 PM PY 407 HW #10 (Sp09) (843690) Fri Apr :00 PM EDT Details TR3 7.P.10. [427795] For a 3p state give the possible values for each of the following orbitals. (Type your answer using hbar for and any integers as necessary. Multiple values must be entered from smallest to largest and separated by commas, for example -1,-hbar,0,hbar,1.) n = 3 -or- +3 = 1 -or- +1 m = -1,0,+1 -or- -1,0,1 L = L z = sqrt(2)*hbar -hbar,0,hbar -or- -hbar,0,+hbar L x and L y are unrestricted except for the following constraint: L x 2 + L y 2 = L 2 - L z 2 L x + L y = L 2 - L z 2 L x 2 + L y 2 = (L z 2 - L 2 ) L x + L y = (L z 2 - L 2 ) 2. Details hydrogen wave function [ ] Use tables 7.1 and 7.2 (on p. 245 of the textbook) to determine the wave function for a hydrogen atom with quantum numbers of! Details TR3 7.P.15. [427731] What is the smallest value that may have if 310 is within 3.25 of the z axis? 90&deployment= &UserPass=3cbbf1beb65596f59524d3adc093453f Page 1 of 2
8 4/6/09 5:42 PM PY 407 HW #12 (Sp09) (852110) Fri Apr :00 PM EDT Details TR3 7.P.34. [696813] Find whether the following transitions (specified in terms of the initial and final quantum numbers n,, m, and m s ) are allowed, and if they are, find the energy involved (whether or not the transition is allowed) and whether the photon is absorbed or emitted for the hydrogen atom. transition B z (T) allowed?!e (ev) (a) (3, 1, 1, 1/2) (6, 0, 0, 1/2) 0 ---Select--- absorbed 1.13 (b) (4, 3, 1, -1/2) (4, 2, 0, -1/2) Select--- absorbed 5.21e-05 (c) (4, 3, -1, -1/2) (5, 3, -1, 1/2) 0 ---Select--- unallowed (d) (5, 2, 0, -1/2) (5, 1, 1, -1/2) Select--- absorbed 2.89e Details TR3 8.P.07. [427714] The 3s state of Na has an energy of ev. Determine the effective nuclear charge e 3. Details TR3 8.P.09. [439999] Select the correct atom for each electron configuration. 1s 2 2s 2 2p ---Select--- B 1s 2 2s 2 2p 6 3s ---Select--- Na 3s 2 3p 6 ---Select--- Ar Name (AID): PY 407 HW #12 (Sp09) (852110) Locked: No Author: Kustusch, Mary Bridget ( mbkustus@ncsu.edu ) Last Saved: Apr 6, :54 PM EDT Permission: Protected Randomization: Person Which graded: Last Publish Essay Scores Help/Hints Publish Essay Scores Help/Hints Key 10&deployment= &UserPass=3cbbf1beb65596f59524d3adc093453f Page 1 of 1
TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 3650, Exam 2 Section 1 Version 1 October 31, 2005 Total Weight: 100 points
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