Why do H2 and H2+ molecules have different vibrational frequencies?

[terp.asessed]

Homework Statement

It's just that I am curious from the vibrational frequency table in the textbook--could someone tell/explain to me why H₂ molecule's vib. frequency is about 4400cm^-1, whereas H₂⁺ is 2300cm^-1? It just seems bizarre to me that such similar molecule should have different vibrational frequency.

Homework Equations

maybe v = ω/(2πc)? I am not sure, but I think the equation is related to my question above.

The Attempt at a Solution

What I am sure of now is that H₂'s vib. frequency is about x2 that of H₂⁺...so I wonder if this problem arises from H₂⁺ having less electron, thus more delocalization between two H nuclei?

 

[Borek]

There are two electrons, to some extent each is responsible for half energy of the bond. When you remove one, there is only "half bond" left.

 

[terp.asessed]

Thank you for the reply! Aside, so, since H₂⁺ has only one electron responsible for the bond, b/c it has to take responsiblity of ALL the bond energy, one electron taking the role of two at the same time, its vibrational frequency is twice the H₂? So, it has nothing to do with angular frequency?

 

[Borek]

Vibrational vs rotational, are you sure you are not confusing them?

 

[OldEngr63]

What kind of frequency has the units cm^(-1)?

 

[Borek]

It is not a frequency. cm^-1 is a unit of describing the wavelength in spectroscopy (in a way similar to Hz describing frequency), and wavelength and frequency are related by $c=\nu\lambda$. A little bit obscure when you are not in the field, but should be clear for every chemist :)

 

[Dr.D]

Thank goodness I'm not a chemist!

It must be extremely confusing to be required to call everything by the wrong name. Why not call it wave length and be done with it?

 

[Borek]

I don't think it is strictly limited to chemistry, more like to spectroscopy (being a chemist I am a little bit skewed). Wavenumber is more convenient than the wavelength as it is directly proportional to energy (which is particularly convenient in the case of the initial question - 2300 cm^-1 is almost exactly half of the 4400 cm^-1. Bingo!