Curious George and the. Choose 3 out of 4 problems Fall 2006 Test 1 09/27/06

Transcription

1 Contemporary Physis SOLUTION KEY Curious George and the. Choose 3 out of 4 problems Fall 006 Test 1 09/7/06 1) Curious George is on a roket ship that is heading out to a planet that is 6 light-years away from Earth. He sends signals bak toward Earth every ship year. The signals (the ones from George s outward journey) are arriving at Earth at a rate of 1 signal every.5 earth years. [Note: years are NOT round numbers in this problem take a deep breath..] a) How fast is George s roket going? 1 u 1 1 u 5.5 f = f 0 = 6.5 ( u) = ( + u) u = = u.5 1+ u 7.5 b) How many Earth years will pass for the round trip journey, and how many ship years? t Earth 1year = = years (16.57) 1 (0.7) = t ship = years ) When George arrives at the planet, he sends an arrival signal bak to The Man in the Yellow Hat (on Earth). In what Earth year will The Man get that signal? Arrival signal starts out in Earth s 8.8 year and takes 6 years to ome bak = 14.8 years on Earth d) At the moment when The Man reeives that arrival signal on Earth, what year is it on the ship (that is, how many years have passed sine the start)? How muh of the Earth time has passed at that point? 14.8/16.57 = 86.% thus t ship = 0.86(11.43) = 9.85 years. ) The Man is doing some partile physis analysis of a banana (hey, you hang around with Curious George, you get some strange ideas for experiments). He has an eletron beam and a muon beam (the muon is an exoti partile and has a rest energy of 105 MeV {and a positive harge}, while the eletron has a rest energy of MeV). a) If he sets the beam speed to be 0.95, how muh kineti energy does eah type of partile (eletron, muon) have? Find total energy for eah subtrat rest energy to find KE: Ee = = MeV KE e = = MeV Em = = MeV KE m = MeV b) Calulate the momentum of eah of the partiles. p = E Eo pe = = 1.55 MeV pe = 1.55 MeV pm= = MeV pm = 319.5MeV ) Suppose a muon hits the banana and bounes bak with the same speed (0.95) toward one of the eletions. With what speed (magnitude) will the eletron pereive the muon to be traveling? [Note, if you answer 1.9, pik up your papers and leave the lass and never ome bak ] And, explain the relative size of your answer (ompared to the other veloities). v u 0.95 (0.95) 1.9 v = = = = ( approahing) vu 1 1 ( 0.95)(0.95) must be greater than 0.95 but less than!! d) The muon and eletron from part B ollide and there is a flash of light and Curious George (who was hanging around hoping to steal the bananna) noties that the partiles disappeared, but only ONE photon resulted. But, Curious George was how shall I put this.. urious as to why there was only ONE photon, when he had heard about pair annihilation needing two photons is something different about this ollision? Also, alulate the energy of the photon and the wavelength of the photon in fm (fm=10-15 m=10-6 nm). You would need two photons if there were no net momentum initially (like in a standard pair annihilation situation) in this ase, there was net momentum (the muon s momentum muh greater than the eletron s) so you ould have momentum onserved with just one photon. 140eVnm 6 Ephoton = = MeV λ = = 3.7x10 nm= 3.7 fm x10

2 3) Curious George deides to set up his own banana experiment, and shines a tunable laser onto the metalli stiker on the side of a banana. (The tunable laser an vary the wavelength between 150 and 500 nm.) For some of the wavelengths, CG noties that there are eletrons released from the surfae of the metal. a) If CG uses a wavelength greater than 400 nm, he finds that there are no eletrons are released. What information does this give us about the metal (it is some weird kind of metal that fell to Earth in the enter of a meteor you don t need to identify whih metal it is). Work funtion of the metal : 140 W = Emin = = 3.1 ev 400 b) If CG uses the 0 nm setting, what is the speed (as a fator of ) and kineti energy of the eletron released? 140 v KE (.54) KE = E W = ev = = = E = 511, 000 = 0 ) In pratie (in the lab), how are these kineti energies determined in an experiment similar to this? (Hint, what is the unit of the energy we use with this model?) By the use of a stopping potential with the eletrons being freed there would be a urrent produed (if the eletrons hit another plate and omplete the iruit if you bias the plates with a tunable voltage you an find the voltage where the eletrons stop arriving at the other plate thus, you must have taken away all the KE released and the ev unit shows that onnetion this eletion and what voltage will stop that KE. d) Another metalli label on a different banana has a stamp on it that says 8.7 ev. Sine that is learly not the prie what ould that indiate about how George must set his tunable laser (or is it even possible to use this laser)? Not possible 8.7 ev requires a maximum wavelength of 14.5 nm smaller than that is fine, but larger means you don t have enough energy to overome the work funtion. Sorry Charlie (I mean, George). 4) The Man throws a small banana hunk (mass=0.33 kg) through a small slit (width of 0. meters) with a speed of m/se. He is trying to demonstrate the wave nature of the banana hunk to Curious George. a) He won t sueed with that partiular experiment explain why not (giving numerial proof). 34 h 6.6x10 Jse 35 = = = 1.0x10 m - this is a fator of 10 0 smaller than a proton slit is WAY too large λ p ( 0.33 kg) ( m/ se) a lassial objet like this will not easily demonstrate its wave nature! b) Instead George takes a moleule of the banana (mass = x10-6 kg) with a speed of m/se. Will he be more suessful with demonstrating the wave nature of that moleule (oh, and George is smart enough to use a smaller slit roughly how small should he use)? 34 h 6.6x10 Jse 6 λ = = = 1.0x10 m= 1000 nm Wavelike! Use a slit larger than 1000 nm, but not too large! p x10 kg (0.033 m/ se) 6 ( ) ) Explain the general idea of Heisenberg s Unertainty priniple and omment on how this might affet attempts to moleularly transport matter from one side of the lab to the other (like the Star Trek transporter ). Heisenberg s Unertainty Priniple puts a pratial limit on how aurate pairs of variables an be measured at the same time (momentum and position, energy and time). You an inrease one unertainty to redue the other, but the produt of the two has a non-zero minimum value. Thus we an t know both of the variables to an arbitrary preision there is a limit. Sine we an t know both position and veloity of all the partiles in a piee of matter even if we ould strip down all the parts and onvert them to information that ould be set aross the room we ouldn t assemble them in exatly the same orientation on the other end. You re not getting me in one of those transporters until they an ome up with some other way to do it that doesn t involve Heisenberg or until they invent the Compensator!!

3 Contemporary Physis Name Curious George and the. Choose 3 out of 4 problems Fall 006 Test 1 09/7/06 1) Curious George is on a roket ship that is heading out to a planet that is 6 light-years away from Earth. He sends signals bak toward Earth every ship year. The signals (the ones from George s outward journey) are arriving at Earth at a rate of 1 signal every.5 earth years. [Note: years are NOT round numbers in this problem take a deep breath..] a) How fast is George s roket going? b) How many Earth years will pass for the round trip journey, and how many ship years? ) When George arrives at the planet, he sends an arrival signal bak to The Man in the Yellow Hat (on Earth). In what Earth year will The Man get that signal? d) At the moment when The Man reeives that arrival signal on Earth, what year is it on the ship (that is, how many years have passed sine the start)?

4 ) The Man is doing some partile physis analysis of a banana (hey, you hang around with Curious George, you get some strange ideas for experiments). He has an eletron beam and a muon beam (the muon is an exoti partile and has a rest energy of 105 MeV {and a positive harge}, while the eletron has a rest energy of MeV). a) If he sets the beam speed to be 0.95, how muh kineti energy does eah type of partile (eletron, muon) have? b) Calulate the momentum of eah of the partiles. ) Suppose a muon hits the banana and bounes bak with the same speed (0.95) toward one of the eletions. With what speed (magnitude) will the eletron pereive the muon to be traveling? [Note, if you answer 1.9, pik up your papers and leave the lass and never ome bak ] And, explain the relative size of your answer (ompared to the other veloities). d) The muon and eletron from part B ollide and there is a flash of light and Curious George (who was hanging around hoping to steal the bananna) noties that the partiles disappeared, but only ONE photon resulted. But, Curious George was how shall I put this.. urious as to why there was only ONE photon, when he had heard about pair annihilation needing two photons is something different about this ollision? Also, alulate the energy of the photon and the wavelength of the photon in fm (fm=10-15 m=10-6 nm).

5 3) Curious George deides to set up his own banana experiment, and shines a tunable laser onto the metalli stiker on the side of a banana. (The tunable laser an vary the wavelength between 150 and 500 nm.) For some of the wavelengths, CG noties that there are eletrons released from the surfae of the metal. a) If CG uses a wavelength greater than 400 nm, he finds that there are no eletrons are released. What information does this give us about the metal (it is some weird kind of metal that fell to Earth in the enter of a meteor you don t need to identify whih metal it is). b) If CG uses the 0 nm setting, what is the speed (as a fator of ) and kineti energy of the eletron released? ) In pratie (in the lab), how are these kineti energies determined in an experiment similar to this? (Hint, what is the unit of the energy we use with this model?) d) Another metalli label on a different banana has a stamp on it that says 8.7 ev. Sine that is learly not the prie what ould that indiate about how George must set his tunable laser (or is it even possible to use this laser)?

6 4) The Man throws a small banana hunk (mass=0.33 kg) through a small slit (width of 0. meters) with a speed of m/se. He is trying to demonstrate the wave nature of the banana hunk to Curious George. a) He won t sueed with that partiular experiment explain why not (giving numerial proof). b) Instead George takes a moleule of the banana (mass = x10-6 kg) with a speed of m/se. Will he be more suessful with demonstrating the wave nature of that moleule (oh, and George is smart enough to use a smaller slit roughly how small should he use)? ) Explain the general idea of Heisenberg s Unertainty priniple and omment on how this might affet attempts to moleularly transport matter from one side of the lab to the other (like the Star Trek transporter ). Honor Code Pledge: "I have neither given nor reeived unauthorized aid in ompleting this work, nor have I presented someone else's work as my own."