# Rotational spectrum - equidistance

• Petar Mali
In summary, the difference between two rotational terms is given by a formula that is valid for the rigid rotor approximation. However, real systems tend not to behave like that except for low rotation numbers. The approximation fails at higher rotation states due to the effect of centrifugal force on the interatomic distance. The equation for the rotational energy and the term values also do not follow an equidistant pattern.
Petar Mali
Difference between two rotational terms is given by

$$\tilde{\nu}=(J+1)(J+2)B-J(J+1)B=2B(J+1)$$

If we put values of $$J$$ in this expression we get that otational spectrum is equidistant.

$$T_r$$ - rotational term
$$J$$ - rotational quantum number

But from this picture spectrum isn't equidistant.

http://www.mwit.ac.th/~physicslab/hbase/molecule/imgmol/rotlev.gif

Can you tell me where is the problem? Thanks!

Last edited:
I can't view the picture. But the equation you cite is valid for the rigid rotor approximation. Real systems tend not to act like that except for low rotation numbers.

alxm said:
I can't view the picture. But the equation you cite is valid for the rigid rotor approximation. Real systems tend not to act like that except for low rotation numbers.

I put the other picture
http://www.mwit.ac.th/~physicslab/hb...mol/rotlev.gif

Look at this picture. You have rotation and vibration levels. Yes I assume that two moleculs system - rigid rotor approximation.

Last edited by a moderator:
Right well what's the question? Why the approximation fails at higher rotational states?

Simply "centrifugal force" - the interatomic distance increases at higher rotation speeds/states, you get a different B.

The centrifugal force is not the case in this picture

$$E_r=J(J+1)\frac{\hbar^2}{2I}$$

$$T_r=\frac{E_r}{hc}$$

For $$J=0$$ $$T_r=0$$

For $$J=1$$ $$T_r=2B$$

For $$J=2$$ $$T_r=6B$$

For $$J=3$$ $$T_r=12B$$

...

It isn't equidistant if I calculate like this. And in picture which you see is this terms. It looks like contradiction if you look this post and my first post!

## 1. What is a rotational spectrum?

A rotational spectrum is a series of spectral lines that represent the different energy levels of a molecule's rotation. These lines are equidistant from each other, meaning that the energy difference between each line is the same.

## 2. How is rotational spectrum - equidistance measured?

Rotational spectrum - equidistance is measured using microwave spectroscopy. This technique involves passing a beam of microwaves through a sample of gas and recording the absorption or emission of energy at different frequencies.

## 3. What causes the equidistance in a rotational spectrum?

The equidistance in a rotational spectrum is caused by the quantized energy levels of a molecule's rotational motion. These levels are determined by the molecule's moment of inertia and the principle of quantization, which states that energy can only exist in discrete levels.

## 4. How does rotational spectrum - equidistance help scientists study molecules?

By analyzing the equidistant lines in a rotational spectrum, scientists can determine the moment of inertia and other properties of a molecule, which can provide valuable information about its structure and behavior. This technique is especially useful for studying gas-phase molecules.

## 5. Can rotational spectrum - equidistance be used to identify unknown molecules?

Yes, rotational spectrum - equidistance can be used for molecular identification. Each molecule has a unique rotational spectrum, allowing scientists to compare and match experimental spectra to known reference spectra to identify unknown molecules.

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