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Homework Set 6 with Solutions - Light Matter Interaction | OSE 5312, Assignments of Chemistry

Material Type: Assignment; Professor: Hagan; Class: Light Matter Interaction; Subject: Optical Sciences; University: University of Central Florida; Term: Spring 2008;

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Pre 2010

Uploaded on 11/08/2009

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Download Homework Set 6 with Solutions - Light Matter Interaction | OSE 5312 and more Assignments Chemistry in PDF only on Docsity! OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Spring 2008 Homework set 6: Due Wed, March. 5 1. Starting from the Debye equation, derive expressions for χ’(ω) and χ”(ω), for a liquid made up of molecules with permanent dipole moment. Methanol is a liquid composed of 1028 polar molecules per m3, each with a dipole moment of 1.7 Debyes (1 Debye = 3.35 x 10-30 C m), and a relaxation time of 50 ps. Taking the high frequency (compared to frequencies relevant to hindered rotational modes) dielectric constant, ε∞ = 2.1, plot χ’(ω), χ”(ω), n(ω) and κ(ω) vs. ω for methanol at T=300 K. (15 points) POLAR DEBYE LIQUID: Methanol «By 3esdd 17 Jy - 26054 (cm einf = 21 act ~ 1.419 x 107 13-108 ..5 = 10! Note: Debye = 335-1077" (em) tsking yf 10"? (percubie meter) sy -ag5007 ee tae Beam eso? =(60 piceseconds) x0 (a) = Rerlo) i, Ingle! eT \l+oa-1r = T T T Lt T T \ T T | Rela) \ Egle) I IP 4 op 4 L L Ne n pk L L Ll rao® ae? i a oe ao pao? pao ao aan! pag? a a | Beele |e 21+Reyc) Imele|= Inyo! ly 2 2 \ ¢ 1 ) ale)» [2 aata) Tnela!” + Reale)! ole! - [3 uy 1 1 T a4 1 T ‘| 1 L ) 02 4 sf) Sie) 0277 ik 4 ! 0 1 - 1 1 1 L - 1g éetio' 3320!" 210! a * yao! usage! zag! ° ® a T T T T pH ase rela) — whe 1 4 1 - 1 o ‘ > Oo A api? rE) tana? tae nae aa0? a0! bao pag? piel! pa tae? 110 ® «ly (ran , we ] mS venrneed — v by \Ertu, Rig ben, Er — Va ey Ca Wonk wo» prt bey 4, Ku I+ $1 +R Are dubs \wak Vt 4-3 4063 = 5-43- ) \ Fete \enkt = 16 aA Os Tg = “14 are 4 = Lol «lo whcc vs a wore vv dle hy von, — —_ 3. A diatomic molecule has atomic masses 4 amu and 10 amu. The atoms are spaced by distance x and the potential energy well they sit in is found to be adequately described by: U(x) = {1(Å5)/x10-1/x5} ⋅2 (kg Å7/s2) where x is in Å. Find the equilibrium spacing, xo. Determine the range over which the potential approximates a harmonic potential, and find the natural vibrational frequency of the molecule in this range. (15 points) Ue» = 2 (45 - >) - Fs [4% - 30) — 2, [22 -) I bALoL > vnbioe _ te Lo &zQ Win imi, Te [pA ae ALL U (2-25) Appel, peal. py we e<purd Iw Tanlors Sere dk Ly? Ur) = UW Soy = UO (xo) + Ax UL (26) ae Uy ) + ox LA (2%) boo ava vee. =O ) Soe U ts pach On a rane wwe. : " d in 2," Ax m a U (0) a) U (2 UW (%) | p- «|Axe | <S 3 Te
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