6.169. M = limd 2 E/2 = 3.5h, where m is the mass of the mole-
cule.
6.170. I = hIAw = 1.93.10-4° g•cm^2 , d = 112 pm.
6.171. 13 levels.
6.172. N^ 1121w1h =^33 lines.
6.173. dN IdE V I 12h 2 E, where I is the moment of inertia
of the molecule. In the case of J = 10 dN IdE =1.0-10^4 levels
per eV.
6.174. Evib/Erot = cottd^2 /h, where p, is the reduced mass of
the molecule; (a) 36; (b) 1.7.10 2 -
'(c) 2.9.10^3.
6.17'5. Nvi b/Nrot = 1/3e-7,0)-2M/11T = 3.1.10-4^ where^ B
h121, I is the moment of inertia of the molecule.
6.176. According to the definitionE E, exp (— EAT) E Ea exp (— aE0)
(E) —
exp (— E v IkT) exp (—cao)where E a = hco (v + 1/2), a = 1IkT. The summation is carried out
over v taking the values from 0 to oo as follows:
(E) a^ In exp (— ccEo) = a^ exp (—aho)/2)
aa 1—exp (—ahco)—^
hco he)
2 + exp (hw/kT)-1 ;
8 (E) R (hwlkT) 2 e")IhT
C voib
—A,
OT otaolla 1)2^ —0.56R,where R is the universal gas constant.
6.177. d=-- V2h/R0co = 0.13 nm, where μ is the reduced mass
of the molecule.
6.178. X, = Xo/(1 o)ko/2J-cc) = 423 and 387 nm.
6.179. w = rcc — Xv)/X,1, = 1.37.10 14 rad/s, x = 4.96 N/cm.
6.180. /,//,.=exp (—hco/kT)=. 0.067. Will increase 3.9 times.
6.181. (a) See Fig. 46a in which the arrows indicate the motion
directions of the nuclei in the molecule at the same moment. The
oscillation frequencies are col, co 2 , co,, with co, being' the frequency
of two independent oscillations in mutually perpendicular planes.
Thus, there are four different oscillations. (b) See Fig. 46b; there
are seven different oscillations: three longitudinal ones (a)„ 6) 2 , ( 0 3)
and four transversal ones (coo 0) 5 ), two oscillations for each
frequency.
6.182. aro = (113-w) do).
6.183. dAT = (S/2nv (^2) ) co do).
6.184. dN = (V In 2 v 3 ) co 2 do).
6.185. (a) 0 = (h,/k) avno; (b) 8 = (hlk) v r47tno; (c) O =
= (h/k) v V6a2no.