C566lecture16

C566lecture16 - 1 C566 Master Lecture Notes Lecture 16 From...

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Unformatted text preview: 1 C566 Master Lecture Notes Lecture 16 From last time: Symmetric top term energies, including centrifugal distortion terms: F(J +1,K) F(J ,K) = 2B(J +1) 4D J (J +1) 3 2D JK K 2 (J +1) For 1 0, K = 0: = 2B 4D J For 2 1 K = 0, = 4B 32D J K = 1, = 4B 32D J 4D JK Dipole moments via Stark Effect Symmetric top in an electric field, E F(J, K, M) = F(E=0) + F(E) = F(J,K) + F(E) F(E) = first order term + second order term = ) 3 2 )( 1 2 ( ) 1 ( ) 1 ( ) 1 ( ) 1 2 )( 1 2 ( 2 ) 1 ( 3 2 2 2 2 3 2 2 2 2 2 2 J J J M J K J J J J M J K J gB E J J EKM M is the quantum number for the projection of total angular momentum onto the field is the permanent dipole moment Selection Rules: J = 1 K = 0 M = 0 if radiation field vector || to E = 1 if radiation field vector to E Microwave spectrometers have parallel alignment: - + - 2 Diagram of the FIRST ORDER splitting of a symmetric top. Only K 0 levels will split, and the K M dependence in the 1 o term means that K = 1, M = 2 and K= 1, M= 2 levels will be degenerate, and shift the energy of the J = 2 level up. For parallel field, K = 0, M = 0 govern transitions between the degenerate pairs in the J = 1 set to the J = 2 set. Transition energies, in a parallel field: = 2B(J + 1) + ) 2 )( 1 ( 2 J J J KM h E 2 1: K = 0 = 2B(J + 1) = 4B K = 1 = 4B + 2 E/6h M = 4B + 2 E/6h for M = 1 4 B + f o r M = 4 B 2 E/6h for M = -1 If E || = 100 V/cm (mild), = 1D 3.3356410 30 Cm (mild) 2 E/6h = 1/3 (3.3310 30 Cm 100 J C-1 cm 1 100cm m-1 )/6.6x10-34 J s ~ 15 MHz (precision ~0.01 MHz) J=1 K=0 J=2 K=0 J=2 K= 1 J=1 K= 1 4B 4B J=1 K=0 J=2 K=0 4B Apply E Apply E Degenerate pairs, with K = +1 or -1; M = 2, 1, 0, -1, -2 Degenerate pairs, with K = +1 or -1; M = 1, 0, -1 ) 1 ( J J EKM 3 Interstellar molecules Observe extraterrestrial molecules by 1. Microwave absorption of background emission (observe blanks in microwave spectrum) 2. Microwave emission A list that includes molecules discovered up to 2005 (excludes recent anion findings by Patrick Thaddeus at Harvard): http://www.cv.nrao.edu/~awootten/allmols.html Diatomic: H 2 AlF AlCl C 2 CH CH + CN CO CO + CP CSi HCl KCl NH NO NS NaCl OH PN SO SO + SiN SiO SiS CS HF SH FeO(?) Triatomics: C 3 C 2 H C 2 O C 2 S CH 2 HCN HCO HCO + HCS + HOC + H 2 O H 2 S HNC HNO MgCN MgNC N 2 H + N 2 O NaCN OCS SO2 c-SiC2 CO 2 NH 2 H 3 + SiCN AlNC SiNC Four atoms: c-C 3 H, l-C...
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This note was uploaded on 01/18/2012 for the course C 566 taught by Professor Carolinechickjarroll during the Spring '11 term at Indiana.

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C566lecture16 - 1 C566 Master Lecture Notes Lecture 16 From...

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