PHYSICS 222 FiNAL EXAM May 7 2010 NAME CLEARLY 10 1 Which of the following statements is true if the intensity of a light beam is increased while its frequency is kept te same a The photons gain higher speeds b the energy of the photons is increased c the number of photons per unit time is increased d the wavelength of the light is increased 1 i Le 4p E 4 i 10 2 How fast would a space ship have to travel so only one year of travel time as measured aboard the spaceship elapses as it goes to a distant star system in a trip that measured from earth takes five years a 5c b c15 c 0 8c d 0 98 c I 3 10 3 One proton is moving at speed 0 4c and another proton is moving at speed 0 8c The ratio of the momentum of the faster moving proton to that of the slower is a 2 0 b 3 l c 4 0 d 4 7 C 10 4 A surface has a work function of 1 7 eV and has light of wavelength 400 nm shone on it What is the energy of the photoelectrons emitted a 1 41 eV b 1 70 eV c 3 11 eV d 4 52 eV L o As x 3XIo U I3bK1e V 1 7e 1t1 eV 10 5 In the non relativistic case doubling the speed of an electron causes its deBroglie wavelength to a double b quadruple c halve d decrease by a factor of four i nIT 2 a I 2 a 4 how many possible values can the magnetic 10 6 If the angular momentum quantum 1 quantum number mi have a 3 b 4 c 8 d 9 71 1 2 3 f A1L21Y ft i J a 3 Z t I a i 2 I DERWATION OF EiNSTEiN S EQUATION Consider a pulse of light with energy AE emitted from the left end and absorbed at the right end of a closed container railroad car for example that is free to move The container has mass M and lengthL Usethefactthatforsuchaclosedsystemthe center of mass must remain fixed and derive AE mc The light emitted and traveling to the right causes the container to move to the left with velocity x Px i Where Px is the momentum and Mthe mass ofthe container Since the magnitude ofthe momentum ofthe container must equal the momentum ofthe light SE Px7 And It takes the light approximately t AE Mc container Thus the container moves to travel the length ofthe iEL Vt Mc 2 Mc If the container moves to the left mass must be shifted to the right to keep the center of mass fixed Thus the light must carry mass IXm to the other end of the container and JVMx LXmL O Then M MI tEL L LL 2 Mc im I 1E Or Mi 2 c This is the Einstein Equation E iXmc 2 25 8 For an infinite square well of width L show that the allowed energies are quantized Start with the time independent Schroedinger equeation and show each step clearly BE NEAT LI li ji qi b 4 t q Ak r cJc z 4 A6t e 4iL e LL t dv Je I L z tr 20 9 A 100 Watt light bulb operates at temperature of 3000K Assuming it loses energy only by radiation calculate the surface area of the filament w r H St rce i A h I I A 667Xl 36 l7 7k1e Ra How 20 10 How many alpha particles are emitted per second by one microgram of 226 many alpha particles will be emitted per second after the original sample has aged 500 years For Ra use 1 374 x 10 s for its decay constant M 6 2 I c A p 2 e I A cy j74 i1 ZXt9