Rotational Spectroscopy is also known as microwave Spectroscopy and is used for bond length calculations

1. BY
DR. BHAVANA P KHOBRAGADE
RDIK AND NKD COLLEGE BADNERA
Rotational Spectroscopy

11. Now J = B J(J+1)
J = 0 J = 0
J = 1 J = 2B
J= 2 J = 6B
J=3 J = 12B
J=4 J = 20B
Energy between two energy levels are not
equal

12. Let consider transition from J’ to J” thus
J = J” - J”
= BJ”(J’’+1) – B J’(J’+1)
= B (J”(J’’+1) – J’(J’+1))
Note that the selection rule is J =  1, where +
applies to absorption and - to emission.
Now let’s consider transition from
J’ = 0 to J” = 1 J = B (1(1+1) – 0(0+1)) = 2B
J’ = 1 to J” = 2 J = B (2(2+1) – 1(1+1)) = 4B
J’ = 2 to J” = 3 J = B (3(3+1) – 2(2+1)) = 6B
J’ = 3 to J” = 4 J = B (4(4+1) – 3(3+1)) = 8B
etc

13. Spectrum appears as below

14. ISOTOPE EFFECT
 If one of the atom in a Hetero nuclear
diatomic molecule is substituted by the
isotope of the same element with higher
mass then the position of absorption line in
the rotational spectra of these two molecule
will be different this phenomena is called
isotope effect

15. ISOTOPE EFFECT
1H1
(atomic no)6C12 (Mass no)
1D2
6C13
The bond length is same for both M1M2 and M1M2’
for M1M2’ --- higher reduced mass
for M1M2’ --- higher moment of inertia
Rotational constant is inversely proportional to
moment of inertia
Rotational constant of a M1M2’will be lower than that of
M1M2 rotational spectra of the shown in figure
H M1 C12 M2
H M1 C13 M2’
μ

 2
1
2
1
m
m
m
m
2
μr
I 
Ic
8π
h
2

B

16. 2B 4B 8B 12B
cm-1 spectrum
2B 4B 8B 12B
cm-1 spectrum
Rotational Spectrum for M1M2
Rotational Spectrum for M1M2’
ISOTOPE EFFECT

17. APPLICATIONS OF MICROWAVE SPECTROSCOPY
Determination of moment of inertia of diatomic molecule
B
Determination of Bond length
2
2
2
1
2
1
μr
r
m
m
m
m
I 



Ic
8π
h
2

Bc
8π
h
I 2

μ
I
r 

18. LIMITATIONS OF MICROWAVE SPECTROSCOPY
• Microwave Spectra : is only for
molecule having dipole
moment
• The sample must be in
gaseous
state