English

Adjective

triatomic

1. (of a molecule etc) consisting of three atoms

   Ozone is a triatomic form of oxygen

See also

• monatomic
• diatomic
• tetratomic

I \, is the moment of inertia of the molecule

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by

L^2 = l(l+1) \hbar^2 \,

where l is a positive integer and \hbar is Planck's reduced constant.

Also, for a diatomic molecule the moment of inertia is

I = \mu r_^2 \,

where

\mu \, is the reduced mass of the molecule and

r_ \, is the average distance between the two atoms in the molecule.

So, substituting the angular momentum and moment of inertia into Erot, the rotational energy levels of a diatomic molecule are given by:

E_ = \frac \ \ \ \ \ l=0,1,2,... \,

Vibrational energies

Another way a diatomic molecule can move is to have each atom oscillate - or vibrate - along a line (the bond) connecting the two atoms. The vibrational energy is approximately that of a quantum harmonic oscillator:

E_ = \left(n+\frac \right)hf \ \ \ \ \ n=0,1,2,... \,

where

n is an integer

h is Planck's constant and

f is the frequency of the vibration.

Comparison between rotational and vibrational energy spacings

The lowest rotational energy level of a diatomic molecule occurs for l=0 and gives Erot = 0. For O2, the next highest quantum level (l=1) has an energy of roughly:

This spacing between the lowest two rotational energy levels of O2 is comparable to that of a photon in the microwave region of the electromagnetic spectrum.

The lowest vibrational energy level occurs for n=0, and a typical vibration frequency is 5 x 1013 Hz. Doing a calculation similar to that above gives:

E_ \approx 3 \times 10^ \ \mathrm \,.

So the spacing, and the energy of a typical spectroscopic transition, between vibrational energy levels is about 100 times greater than that of a typical transition between rotational energy levels.

Further reading

• Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules
• Physics For Scientists and Engineers : Vol. 1 (4th ed.)

See also

• AXE method
• Octatomic element

Notes and references

External links

• Hyperphysics - Rotational Spectra of Rigid Rotor Molecules
• Hyperphysics - Quantum Harmonic Oscillator
• 3D Chem - Chemistry, Structures, and 3D Molecules
• IUMSC - Indiana University Molecular Structure Center