set1-06-sol

set1-06-sol - Problem 2: Hydrogen atom (10 P) 1) The energy...

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Astro 346, Spring Semester 2006 Homework, 1st set, solutions. Problem 1: Relativity (10 P) 1) Use Taylor expansion! γ 1 + β 2 2 E = m 0 c 2 + T γ m 0 c 2 = m 0 c 2 + m 2 β 2 c 2 T = m 2 v 2 Also γ = s 1 + p 2 m 0 c p = m 0 c q γ 2 - 1 = m 0 c β q 1 - β 2 = γ m 0 v m 0 v 2) Let the stationary frame be K and the car’s rest frame K 0 with the car located at the origin, x 0 = 0 . We can use the approximate form for γ derived in part 1). Then, if both clocks were set to zero at the time of departure, upon arrival one would measure t = γ t 0 δt = t - t 0 = ( γ - 1) t 0 v 2 2 c 2 (10 hours) 2 . 2 · 10 - 10 sec Only atomic clocks have the accuracy required to measure this eFect. The example is prob- lematic on account of the earth rotation, because it causes the motion to change direction.
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Unformatted text preview: Problem 2: Hydrogen atom (10 P) 1) The energy is E = 13 . 6 eV 2 . 2 10-18 J = 2 . 2 10-11 erg The frequency and wavelength are derived using = E h 3 . 3 10 15 Hz = c 10-7 m = 100 nm This frequency corresponds to hard UV radiation. To ionize the atom radiation must have at least a photon energy of E = 13 . 6 eV , that is it must be hard UV, X-ray, or gamma radiation....
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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