Negative Exponent Explained: 300 cm-1 Meaning

[Drakkith]

I've seen the use of a negative exponent in the books and articles I've been reading lately, and I was wondering exactly what it meant. Such as 300 cm-1, where cm has a -1 as the exponent. (Dont know how to type that out.) What does it mean?

 

[LeonhardEuler]

It means the same thing as $\frac{1}{cm}$. For instance, $3m s^{-1}$ means the same thing as $3\frac{m}{s}$

 

[Drakkith]

Hrmm. I just read something where the distance between two atoms was 3000 cm-1. Surely that can't be 3000 over 1?

 

[LeonhardEuler]

That can't be right for a distance. Can you give the exact sentence?

 

[Drakkith]

Sure, here it is.

"Since both rotational and vibrational motions are simultaneously occurring in the diatomic, the energy level scheme for two adjacent vibration levels (spaced, say, 3000 cm-1 apart) where ca. 10 cm-1 in the two states, would be as shown in Fig. 1."

From the article here: http://www.chem.ufl.edu/~itl/4411L_f00/hcl/hcl_il.html

Edit: Copy and Pasting didn't keep the exponents like they were in the article, as they now look like I typed it out.

 

[LeonhardEuler]

Ok, it's not a measurement of the physical distance between atoms, it's a measure of the difference in frequency between the radiation emitted by two modes of vibration of the pair of atoms. This measurement is called the "wavenumber":
http://en.wikipedia.org/wiki/Wavenumber
The higher the wavenumber, the higher the energy of the vibration.

 

[Drakkith]

Ah, ok. That makes perfect sense now. I've been reading some things on quantum physics and such, and I had never seen that before. Thanks!

 

[gb7nash]

Sure, here it is.

"Since both rotational and vibrational motions are simultaneously occurring in the diatomic, the energy level scheme for two adjacent vibration levels (spaced, say, 3000 cm-1 apart) where ca. 10 cm-1 in the two states, would be as shown in Fig. 1."

From the article here: http://www.chem.ufl.edu/~itl/4411L_f00/hcl/hcl_il.html

Edit: Copy and Pasting didn't keep the exponents like they were in the article, as they now look like I typed it out.

http://en.wikipedia.org/wiki/Wavenumber

It's used for the wavenumber, which is proportional to the reciprocal of the wavelength (which is measured in cm). Why wavenumbers are important isn't a question I could answer. I forgot a lot of physics. =(

Euler beat me!

 

[Drakkith]

http://en.wikipedia.org/wiki/Wavenumber

It's used for the wavenumber, which is proportional to the reciprocal of the wavelength (which is measured in cm). Why wavenumbers are important isn't a question I could answer. I forgot a lot of physics. =(

Euler beat me!

Thanks to you too nash. =)