Unformatted text preview: _ EE540 8('11) Midterm Examination. Monday, March 7 (2011). 80 minutes, 2 to 3:20 PDT. p.1 of 3,, EXAM INSTRUCTIONS: Bring to the exam desk only pens, pencils and calculators. Paper on which
you are to submit your answers will be supplied. You may keep the exam problems. Each numbered
problem will be graded 1 to 10. Draw a box around each answer that has its problem number clearly
indicated. Do not change the definitions of any symbols defined anywhere in the exam pages, either
explicitly, implicitly or by their context. You may define new symbols, or make additional assumptions,
inside boxes with a double—line border. Units will always be assumed to be 8.1. Units unless stated
otherwise. The word 'find' in a problem means write a Matlab ready formula in which all quantities . have either been given, or been asked for in earlier problems. The word “calculate in a problem
means ‘use a calculator to obtain a numerical result from a formula’. The word estimate in a problem
means calculate by hand knowing that an answer within a factor of 2 of the machine answer gets full
credit.  * Introduction to Problems [1] to [4]. In “NATURE" vol.311, p132 (1984) the astronomers Joseph, Wright and Wade describe
spontaneousemission lines they observe from hydrogen molecules (H2) that they estimate to be 3
million light—years away, in the galaxy NG06240 The most intense of these lines was the well—known
rovibrational H2 line called the 8(1) line at A..." _ 2. 122 microns 0/1; =— 141 THz). The total power 50
radiated from NG06240 into this 8(1) line must have been ~4E34 Watts according to the “inverse— square law for intensities. (This power is 100 million times larger than the power at all wavelengths of
the light radiated by our sun.) Googling reveals that the Einstein A—coefficient for this 8(1) transition is
A," :?x!o7 .5 and its upper— and lower level degeneracy factOrs 3. and 3& are 3 and 10
respectively. [We will often abbreviate “the 8(1) transition” by “8(1)”] From the relative strengths of
the various H2 rovibrational lines that Joseph, et al., observed, they concluded that the radiating gas
was near thermal equilibriumat T: 5000 K. In problems [1] to [5], assume that this hot gas was uniformly distributed in a spherical shell of , 3
radius Cand volume tfﬂC‘a (This shell of hot molecules may have been the shock wave (8 << 1 ) EC caused by a “super” supernova explosion' In the distant past.) Assume also that the thickness of this
Shell is small enough that every spontaneously emitted 8(1) photon radiated from it escapes into intergalactic space or back into the galaxy body. Then in each of problems [1] to [5] you are to find
(for 8 points) and calculate (for 2 more points) the following: [1] the stimulated emission cross section 0’57 of the S( 1) transition [2] the total number n, of H2 in the upper level (i) of the 8(1) transition [3] the (negative) inversiOn density N ,7 of 8(1) [4] the (positive) absorption coefficient aij at frequency )2” when the actual number density NH of
interstellar hydrogen, as well as its energy levels Ek , are known. [5] the number of 8(1) photons that are received from NGC6240 during 12 hours of observation by
the 30m diameter Keck telescope. Bahmann Constant Agni 38 ”Owes :7'/I<  C73x/0 ms . .
F[a"d"5 Cénﬁllalﬂf' A: 6 626x/0 5343’s 6:: [.éx/Oﬂl? Gdﬁmés‘ ...
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 Spring '08
 Hellwarth

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