# Solved problems - Spectroscopy

```• The first line in the pure rotational spectrum of HCl
appears at 21.18cm‐1. Calculate bond length of the
molecule. Given atomic masses off H and Cl are 1.008
and 35.45 amu respectively.
The microwave
Th
i
spectrometer
t
t capable
bl for
f operating
ti only
l between
b t
60 and
d 90 cm‐11 was used
d
to observe the rotational spectra of HI and DI. Absorption was measured as follow
HI (cm‐1)
DI (cm‐1)
64 275
64.275
65 070
65.070
77.130
71.577
89.985
78.094
84 591
84.591
Find B,I and r for each molecule, and determine the J values for the first lines listed above.
Do your result support the usual assumption that bond length is unchanged by isotopic
substitution?
• For a certain rotationally active molecule the
ʋ(MHz)vs J plot showing a slope of 8603MHz.
C l l t the
Calculate
th rotational
t ti
l constant
t t for
f the
th molecule
l l
and also the rotational quantum number for the
highly populated state at 298K
and 100K?
• A space probe was designed to see CO in
the atmosphere of Saturn by looking for
lines in its rotational spectrum. If the bond
length of CO is 112.8 pm, at what wave
number
b do
d the
th first
fi t three
th
rotational
t ti
l
transitions appear?
pp
What resolution would
beneeded to determine the isotopic ratio
of 13C and 12C on Saturn by
observing three rotational lines
The moment of inertia about an axis perpendicular to principal axis for NH3 is
2.82*10‐47 kg m2. NH3 is which type of rotor? Calculate the separation (expressed in
cm‐11) off the
h pure rotational
i
l spectrum lines
li
f NH3. (the
for
( h moment off inertia
i
b
principal axis given by Iǁ = 2mHR2(1‐cosϴ) where the mass of hydrogen atom mH
=1.6735*10‐27 kg, the N‐H bond length r= 1.014*10‐10 m and the bond angle is
106 780 The moment of inertia abo
106.780.The
a is is Iǁ)
• HCl has a B value of 10.593 cm‐1 and a
centrifugal distortion constant D of
5 3*10
5.3
10‐4
4 cm‐11 estimate the vibrational
frequency and force constant of the
molecule?
The transition moment integral or the probability of transition between two rotational
levels in a linear molecule may be assumed to depend only on the permanent electric
dipole moment of the molecule and thus to be the same for all allowed pure rotational
transitions .In the pure rotational emission spectrum of H35Cl gas , lines at 106.0 cm‐1 and
233.2 cm‐1 are observed to have equal intensities. What is the temperature of the gas?
The Rotational Constant B for H35Cl is 10.6 cm‐1 and the ratio of hc/k is 1.44
The rotational constant of NH3 is equivalent to 298 GHz. Compute the separation of the
pure rotational spectrum lines in GHz
GHz, cm‐11, and show that the value of B is consistent with
an N‐H bond length of 101.4 pm and a bond angle of 106.78&deg;.
Estimate the centrifugal distortion constant for 79Br81Br,for
Which B = 0.0809cm
0 0809cm‐1 and γ = 323.2
323 2 cm‐1. By what factor
Would the constant change when the 79Br is replaced by 81Br
The wavenumber of the incident radiation in a Raman
spectrometer is
i 20487 cm‐11. What
Wh is
i the
h wavenumber
b off the
h
scattered stokes Radiation for the J=0 to J=2 transition for 14N2
The first three lines in the R branch of fundamental
Vibration‐Rotation band for H35Cl have the following
Frequency in cm‐1: 2906
2906.25
25 (0)
(0), 2925
2925.78
78 (1)
(1), 2944
2944.89
89 (2)
Where the number in parentheses are the J values for the
Initial levels
levels. What are the values of γ0 (cm‐1 ),
) Bv’, Bv’’, Be
and α
For 14N2, the Δγ values for the transitions v= 0 – 1, v= 0‐2 and
v= 0‐ 3 are respectively, 2345.15, 4661.40 and 6983.73 cm‐1
Calculate γe, xe, dissociation energy (D0) for the molecule.
Calculate the percentage difference in fundamental vibration
Wavenumber of 1H35Cl and 2H37Cl on the assumption that
Their force constants are same.
```