# Moecular spectroscopy

1. Nov 25, 2005

### photon79

Why is it not possible to obtain a pure vibrational spectrum(IR-spectrum) of a molecule? (vibrational spectrum always contains lines of rotational energies)

2. Nov 25, 2005

### Gokul43201

Staff Emeritus
That's because typical rotational energies (or energy eigenvalues) are of the same order of magnitude as the energies for vibrational and bending (or "breathing") modes for most common organic molecules. How do you excite a molecule to undergo vibrations without undergoing rotation ? If I'm not mistaken, in most cases, that would require a violation of angular momentum conservation.

3. Nov 26, 2005

### photon79

But rotational energies or in microwave region and vibrational are in infrared!

Why is it so that rotation must be excited inorder to excite vibration?

4. Nov 26, 2005

### Gokul43201

Staff Emeritus
What are some typical values for the energy/wavelength of the principal rotational mode vs. the principal vibrational mode. I thought they were maybe, an order of magnitude apart, not much more. Remember, the IR region and microwave region actually have an overlap.
I think, and my recollection is not great, that the main concern here is conserving angular momentum. Imagine an large model of an asymmetric molecule like H2O, floating in the air. Now fire a ball at it and hit the molecule, so that the ball essentially stops after hitting the molecule. Depending on the orintation at which the ball hits the molecule, it will excite different vibrational modes, but will also set the molecule spinning. If the molecule didn't spin, angular momentum would not be conserved.

While this is nothing but a hand-waving argument, it provides a useful analogy.

5. Nov 26, 2005

### photon79

Finally how this angular momentum is conserved by the excitation of rotation?

6. Nov 26, 2005

### Gokul43201

Staff Emeritus
I can provide a classical analogy.

Imagine a rod of length L and mass M, at rest on a smooth, frictionless floor. Imagine a smooth ball of mass m, approaching this rod at velocity u. It strikes the rod at a distance r from the center of mass (CoM) of the rod, and comes to rest following this elastic collision. The rod starts moving as a result.

Then linear momentum conservation will give :

$$mu = Mv_{rod}$$

And angular momentum conservation will give :

$$mur = I_{rod}\cdot \omega_{rod}$$

Thus, to conserve angular momentum, the rod must have some anglar velocity $\omega_{rod}$ after the collision.

Now replace the rod with a molecule, and the ball with a photon. A similar happens in this case too (except that, with the rod, vibration and bending was not allowed; with the molecule, it is allowed)

Last edited: Nov 26, 2005