23.3 Rotational and Vibrational Spectra of Diatomic Molecules 963
42302012E
/hB6
2
0
(a)Absorbance(^02) B~e 4 B~e 6 B~e 8 B~e 10 B~e 12 B~e 14 B~e
n5~^1
(b)
Figure 23.7 A Microwave Spectrum.(a) The allowed transitions. (b) The simulated
spectrum. The positions of the spectral lines are correlated with the transitions that produce
the lines.
Solution
The splitting is equal to 2 ̃Be, so the value of ̃Be 1 .9313 cm−^1 , in agreement with the value
in Table A.22 of Appendix A. We assume that the molecule contains the isotopes^12 C and
(^16) O, with masses 12.0000 amu and 15.994915 amu.
μ
(
(12.0000 amu)(15.994915 amu)
12 .0000 amu+ 15 .994915 amu
)(
0 .001 kg
6. 02214 × 1023 amu
)
1. 1385 × 10 −^26 kg
r^2 e
h
8 π^2 μ ̃Bec
6. 6261 × 10 −^34 Js
8 π^2 (1. 1385 × 10 −^26 kg)(1.9313 cm−^1 )(2. 9979 × 1010 cm s−^1 )
1. 2731 × 10 −^20 m^2
re
√
- 1283 × 10 −^20 m^2 112. 83 × 10 −^10 m 1 .1283 PM 1 .1283 Å