Page 1 of 4 PHY3101 2-10-99 Name:_______________________ SSN: ________________________ Midterm 1 Closed book exam. One 8.5x11" study sheet is allowed. A calculator is allowed also. Exam is worth 30 points, 15% of your total grade. 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 light-year = 09461016.×m 1 year = 316107.×s e2094144 10πε= ×−. eV- m FEvB=+×q() WqV= γ =−112 2v c/ ′ = −′ = −x x vtt t vx cγγbgc h/2 ′=′=y yz z tt=γ 0 LL=0γ E mc= γ2 K mc= −γ 12bg pv=γm Fp=ddt/ υββυ=±110m β =vc m c E p c2 4 2 2 2= − ame00221040 53 10= = ×−πεh. m EZ e mn nne=−= −2 4202 2 22 4136h ( ).πε eV Z2b g REhc∞= = ×07109737 10. m-1 REhcH= = ×07109678 10. m-1 λ m- KT = ×−2 898 103. eVh0=−υφ ∆λ θ= −hmc1 cosbg 1 1 12 2λ= −FHGIKJRn nl u λT = ×−2 898 103. m- KPage 2 of 4 PHY3101 2-10-99 Name:_______________________ SSN: ________________________ 1. You want to travel to the center of our galaxy to visit a massive black hole (Sagittarius A). The distance to the galactic center from Earth is 100,000 light-years, as measured in the rest frame of the galaxy. (1 light-year = 9461015.× m) (a) [4 points] By how much must the distance be contracted so that you can reach the galactic center within your lifetime (assume 100 years) on a spaceship travelling at a constant velocity? That is, what is the necessary relativistic factor γ? (b) [4 points] If you transmit radio messages to Earth at a frequency of 1 GHz (109 Hz) during the trip, at what frequency are they received on Earth? Assume that there will be someone there to receive them! (c) [4 points] If the black hole consumes you and your ship (M = 106 kg), how much energy will be absorbed? Ignore any acceleration.Page 3 of 4 PHY3101 2-10-99 Name:_______________________ SSN: ________________________ 2. [4 points] Light with a frequency of 1.38×1015 Hz ejects photoelectrons from a magnesium photocathode with a work function φ = 3.7 eV. What stopping potential is required to stop the photoelectron current between the cathode and an anode? 3. [4 points] An x-ray Compton scatters 180° off an electron at rest. That is, it scatters in a direction opposite the incident direction. If the initial wavelength is 0.05 nm, and the final wavelength is 0.055 nm, what is the momentum of the electron after the scattering? 4. [4 points] A hydrogen atom in its ground state absorbs a photon of wavelength 97.2 nm. What excited state will the atom find itself in after absorption?Page 4 of 4 PHY3101 2-10-99 Name:_______________________ SSN: ________________________ 5. [6 points] Name 3 crises in classical physics (Newtonian mechanics, electromagnetism, and thermodynamics) which require new laws of physics. Explain each problem and its