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.



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 :



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



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)



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

ep- molecular spectra-end sem -student handout-2014

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