# Negative Exponent

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

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

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

Staff Emeritus
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.

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LeonhardEuler
Gold Member
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.

Staff Emeritus
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
Homework Helper
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!

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