Page 1 of 6 PHY3101 4-29-99 Name:_______________________ Final Exam Closed book exam. One 8.5x11" study sheet is allowed. A calculator is allowed also. Exam is composed of 12 problems worth 60 points, 30% of your total grade. Formulas and constants are on both sides of this first page. Forms of the Schrodinger equation: −∂∂+ =∂∂− + =hhh2 222 222 2m xV x t it mddxV x Eψψψ ψψ ψ( , ) ( ) Constants and equations: h=×−662611034. J-s c=×30108.m/s e=×−160221019. C h=×−413571015. eV-s λν = c 1 eV J=×−160221019. hc=1240 eV-nm Eγ = h ν 1 MeV = 106 eV h = = ×−h / .2 10546 1034π J - s λ = h / p 1 nm = 109−m h = ×−65821 1016. eV -s 1 Watt = 1 J/s 1 MHz = 106s-1 me= ×−911 1031. kg mp= ×−1673 1027. kg mµ= ×−1881 1028. kg me=0511. MeV / c2 mp=9383. MeV / c2 mµ=1057. MeV / c2 1 u kg= ×−16605 1027. 1 u MeV/=93152.c v = H0 r H0 = 65 km/s/Mpc λT = ×−2 898 103. m- K 1 326 106 Mpc = light - years. × 1 light-year = 09461016.×m z = + − −1 1 1β βbgbg/ E p c m c22224= + γβ=−112 β =vc E m c K m c= = +γ 22 e2094144 10πε= ×−. eV- m FEvB=+×q() WqV= REhc∞= = ×07109737 10. m-1 REhcH= = ×07109678 10. m-1 1 1 12 2λ= −FHGIKJRn nl u ame00221040 53 10= = ×−πεh. m EZ e mn nne=−= −2 4202 2 22 4136h ( ).πε eV Z2b g µBeem= = ×−h257884 105. eV / T ∆∆xp ≥h/2 ∆∆Et ≥h/2 f x x f x x dx( ) ( ) ( ) ( )*=zψ ψ I x x dxnnnnn n= − =⋅ ⋅ −⋅+∞zexp( )( / ) ( / )ααπα for even 22 1 201 3 5 12c hL I012=πα dx xxxsin sin22142z= − dx x xx xxx x 2 2326418224sin sincosz= − −FHGIKJ− E-mail: (optional, for grade notification)Page 2 of 6 PHY3101 4-29-99 Name:_______________________ 1. [5 points] You are the captain of a starship travelling at a constant velocity of 0.98 c toward Earth. Your ship’s engineer informs you that the engines will explode in 2 minutes. You need to get to Earth so that you can instantaneously beam off the ship, but you only just crossed the orbit of Mars. In the rest frame of the solar system, calculate the distance you can travel before the engines explode. Will you be able to reach Earth? The orbital radius of Earth is 1 AU, and the orbital radius of Mars is 1.5 AU, where 1151011 AU m=×.. 2. [5 points] The work function of Aluminum is 4.1 eV. Calculate the maximum kinetic energy of electrons ejected from the metal when ultraviolet light with a wavelength of 200 nm shines on the surface.Page 3 of 6 PHY3101 4-29-99 Name:_______________________ 3. [5 points] Calculate the deBroglie wavelength of an electron travelling at a velocity of 86105.× m/s. 4. [5 points] The mean lifetime of the Z0 particle (a force carrying particle of the weak nuclear force) is only 131025.×− s. The mean mass of this particle is measured to be 91 GeV/c2, but because of the finite lifetime there must be some spread around this value for every particle measured. Estimate this spread. (1 GeV = 109 eV) 5. [5 points] An electron in the n = 3 excited state of hydrogen makes a transition to the ground state. What is the wavelength of the photon emitted in the transition?Page 4 of 6 PHY3101 4-29-99 Name:_______________________ 6. [5 points] The wavefunction for a particle in a particular potential well is given by ψ αx A xbgch= −exp / 22 , valid for all real x. Normalize this wavefunction and determine the constant A. 7. [5 points] Plug the wavefunction ψ αx A xbgch= −exp / 22 into the time-independent Schrodinger Equation and determine what the potential energy function must be and what the total energy of the particle is.Page 5 of 6 PHY3101 4-29-99 Name:_______________________ 8. [3 points] Write down the electronic configuration for an atom of Chlorine (atomic number Z = 17) in the ground state (i.e. He = 1s2) . 9. (a) [2 points] Fill in the missing nucleus in the following reaction: 1324H He+ → +ZAX n (b) [3 points] For whatever choice you made in (a) calculate the energy released or absorbed in the reaction. 10. [4 points] Explain why each of the following reactions is forbidden (a) ppppn+→++ (b) µ γ− −→ +e (c) π−+ →p K0 (d) n p e→ +−Page 6 of 6 PHY3101 4-29-99 Name:_______________________ 11. [5 points] The spectral lines emitted by a distant galaxy are observed to have a redshift factor of 0.5. How distant is the galaxy? You may assume a Hubble constant of 65 (km/s) / Mpc , where 1 326 106 Mpc = light - years. × and 1 light-year is 09461016.×m. You may also find the following formula useful: z = + − −1 1 1β βbgbg/ 12. [8 points] Give at least one reason for each of the following (you may use the back of the page) (a) What evidence do we have that nuclear fusion takes place in the Sun? (b) What evidence do we have for quarks? (c) How does the Ω− particle (quark composition = sss) circumvent the Pauli-Exclusion principle? (d) What evidence do we have for the Big Bang model of the