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Unformatted text preview: Ben Sauerwine Practice for Qualifying Exams Problem Source: CMU August 2003 Qualifying Exam Consider a supernova explosion occurring at a known distance D from Earth. The energy spectrum of the photons received on Earth is measured and photons of energies ranging from one electron volt (eV) to a million electron volts (MeV) are detected. Suppose further that all of these photons arrive within a time of each other. We can use this to put upper bounds on the rest mass of the photon. T Δ γ m (a) What is the relativistic relation E(v) between energy E and speed v for a particle with rest mass ? γ m 2 2 2 1 1 c v mc E − = = γ γ (b) If we assume that the rest energy of the photon is much less than one eV, use part (a) to argue that to lowest order, ( ) 2 2 2 1 1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ≈ E c m c E v γ ( ) ( ) ... 2 1 1 1 ... 1 1 1 2 1 2 1 2 1 1 1 1 1 1 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 + − ≈ − + ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ − − − − + ⎥ ⎦...
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 Spring '12
 Dr.Jaouni
 Energy, Mass, Photon, Ben Sauerwine, rest mass mγ

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