# Rotational energy levels of NH3

• _Andreas
In summary, the conversation was about calculating the rotational energy levels of NH3, with the equation EJK = hcBJ(J+1) + hc(A-B)K^2. The question was whether there is a limited set of levels or an infinite number, and it was compared to the energy levels of electrons in an atom. The person asking for help had already solved the problem but apologized for potentially wasting the expert's time. The expert did not mind and was happy to review the concept.
_Andreas
I'm supposed to calculate the rotational energy levels of NH3, which is a symmetric rotator. The rotational energy levels are determined by the equation

EJK = hcBJ(J+1) + hc(A-B)K^2, where J = 0, 1, 2,..., and K = 0, +/-1, +/-2,..., +/-J

I don't quite get it. Are there a very limited set of rotational energy levels for NH3 that makes it practically possible for me to calculate each one of them, or should I calculate only the, say, first four possible levels? I've looked around for clues in my textbook, but I can't see that there are any.

With no upper limit on J there are infinitely many energy levels. This is similar to the energy levels of electrons in an atiom. Start at the bottom and work your way up.

I had already solved it myself before you responded, but thanks anyway! I'll probably need more help in the future.

Oh, I guess I should make it clear if I no longer need help with a problem I've asked for help solving. It's certainly not OK for me to waste your time. My apologies!

_Andreas said:
Oh, I guess I should make it clear if I no longer need help with a problem I've asked for help solving. It's certainly not OK for me to waste your time. My apologies!
It would be good of you to do that. Not a problem here since I did not do much work and needed a bit of review anyway.

## 1. What is the significance of rotational energy levels in NH3?

The rotational energy levels of NH3 are important because they determine the rotational motion of the molecule. This motion is crucial in understanding the physical and chemical properties of NH3, such as its reactivity and spectroscopic behavior.

## 2. How many rotational energy levels does NH3 have?

NH3 has three rotational energy levels, as it is a triatomic molecule. These levels are determined by the number of rotational axes and the symmetry of the molecule.

## 3. How does the energy of rotational levels in NH3 change with temperature?

The energy of rotational levels in NH3 increases with temperature. As the temperature increases, the molecules have higher kinetic energy, resulting in faster rotational motion and higher energy levels.

## 4. How do the rotational energy levels of NH3 affect its heat capacity?

The rotational energy levels of NH3 contribute to its heat capacity, which is the amount of heat required to raise its temperature by 1 degree. As the molecule absorbs heat, its rotational energy levels increase, leading to an increase in heat capacity.

## 5. What is the difference between the rotational energy levels of para-NH3 and ortho-NH3?

Para-NH3 and ortho-NH3 are two different spin isomers of NH3. The rotational energy levels of para-NH3 are evenly spaced, while those of ortho-NH3 are unevenly spaced. This is due to the different orientations of the nitrogen and hydrogen atoms in the two isomers.

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