EP- Molecular Spectra-End Sem -Student Handout-2014
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Transcript of EP- Molecular Spectra-End Sem -Student Handout-2014
8/12/2019 EP- Molecular Spectra-End Sem -Student Handout-2014
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Rotational Spectra Vibrational Spectra
The expression for the rotational energy
levels is given by:
=ħ
+ , where J=0,1, 2…
The expression for the rotational energy levels
is given by:
= +
, = , , , ____
The spacing between the adjacent rotational
levels become far apart with the increase of
the rotational quantum number
The spacing between the adjacent vibrational
levels are equal.
The transition between adjacent rotational
energy levels result in radiation that lies in the
microwave range of frequencies (f~109 Hz)
The vibrational transition photons of a
diatomic (or linear) molecule lie in the infrared
region of the spectrum(f~1011 Hz)
The energy separation between successive
rotational level is much smaller than the
separation between successive vibrational
levels. This means that at ordinary
temperature most molecules are in ν=0
vibration state with zero point energy, but
these molecules can be in various rotation
states.
At room temperature, most of the molecules
have vibrational energies corresponding to the
ν=0 state i.e. vibrational transitions are
forbidden at room temperature. This is
because the spacing between vibrational
states is much greater than the thermal energy
(kBT) at room temperature.
8/12/2019 EP- Molecular Spectra-End Sem -Student Handout-2014
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Molecular Spectra
Absorptive transitions between
the v = 0 and v = 1 vibrational statesof a diatomic molecule.
Expected lines in the absorptionspectrum of a molecule. These same
lines appear in the emission spectrum.
Total energy of a molecule :
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Problem-1: The moment of inertial of the CO molecule is 1.46x10-46 kg-m2.Calculate the energy in eV and the angular velocity in the lowest rotationalenergy level of the CO molecule.
Ans: E=7.6x10-23 J or, 4.75 x 10-4 eV
ω = 10.2 x10-11 rad/sec
Hint: The Lowest rotational energy level will be J=1 state
Because for J=0, E J = 0 and the minimum molecular energy is vibrational
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Problem-2: In the near infra-red spectrum of HCl molecule there is single
intense band at 2885.9 cm-1
[wave number]. Assuming that it is due to thetransition between the vibration levels, show that the force constant k is480Nm-1 (Given MH = 1.68 x 10-27 kg)
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Problem-3: The force constant of the bond in CO molecule is 187 Nm-1
.Calculate the frequency of vibration of the molecule and the spacing between its vibrational energy levels in eV. Given that the reduced massof CO=1.14x10-26 kg: h=6.6 x 10-34 Js and 1eV= 1.60x10-19 J.
Ans. υ = 2.04x 10-13 Hz
ΔE = 8.44 x10-2 eV