6.169. M = limd2E/2 = 3.5h, where m is the mass of the molecule.
6.170. I = hIAw = 1.93.10-4° g•cm2, d = 112 pm.
6.171. 13 levels.
6.172. N
1121w1h = 33 lines.
6.173. dN IdE V I 12h2E, where I is the moment of inertia
of the molecule. In the case of J = 10 dN IdE =1.0-104 levels
per eV.
6.174. E vib/Erot = cottd2/h, where p, is the reduced mass of
the molecule; (a) 36; (b) 1.7.102'
(c) 2.9.103.
6.17'5. N vib/N rot = 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 definition
E 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:
a
a
exp (—aho)/2)
(E)
In
exp (— ccEo) =
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
— X v)/X,1, = 1.37.1014 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, co2, 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/2nv2) co do).
6.184. dN = (V In2v3) co2 do).
6.185. (a) 0 = (h,/k) avno ; (b) 8 = (hlk) v r47tno ; (c) O =
= (h/k) v V6a2no.