Howard University - ADVANCED TOPICS IN LASER SPECTROSCOPY I - PHYS 286

ADVANCED TOPICS IN LASER SPECTROSCOPY I PHYS 286

Fall 2002

Homework #2

Dr. P. Misra

1. The Deslandres Table below summarizes some of the bands observed in the A-X electronic transition for a diatomic molecule (in units of cm^-1):

v’’	0	1	2	3
v’
0		62, 601.8	60,484.7	58,393.2
1	66,231.3	64,087.6		59,881.6
2	67,674.8	65,533.1	63,416.1	61,325.2
3	69,087.8	66,944.3	64,828.1

Using the above data, calculate the wavelengths of the fundamental (1-0) band and the first overtone (2-0) band. In which region of the electromagnetic spectrum are these observed bands present?

2. Figure 1 shows a spectrum of the vibration-rotation bands of the carbon monoxide (CO) molecule observed in emission in the first overtone region around 2.3 mm in the infrared. Because the source gave strong CO emission, it has been possible to observe very high J values as a result of which one can easily recognize the band head formation in each case. [Note that the spectrum is continuous from 4150 cm^-1 to 4360 cm^-1 and has been reproduced in three segments]. The spectral positions that you can determine from the wavenumber scale on each segment are adequate for answering the following questions. Be sure to give reasons to support you answer.

(a) Identify the bands observed in the spectral interval 4250-4360 cm^-1 by giving the vibrational quantum numbers v’ and v’’ in each case.

(b) Give the branch designations (i.e. P, Q, or R) and the J assignments for the two groups of five lines marked Group A and Group B in Fig. 1.