# Dictionary Definition

diatomic adj : of or relating to a molecule made up of two atoms; "a diatomic molelcule"

# User Contributed Dictionary

## English

diatomic
1. (of a molecule etc) consisting of two atoms

# Extensive Definition

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.

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

## Notes and references

• Hyperphysics - Rotational Spectra of Rigid Rotor Molecules
• Hyperphysics - Quantum Harmonic Oscillator
• 3D Chem - Chemistry, Structures, and 3D Molecules
• IUMSC - Indiana University Molecular Structure Center
diatomic in Arabic: ثنائي الذرة
diatomic in Catalan: Molècula diatòmica
diatomic in Spanish: Diatómico
diatomic in Malayalam: ദ്വയാണുതന്മാത്ര
diatomic in Japanese: 二原子分子
diatomic in Russian: Двухатомная молекула
diatomic in Chinese: 双原子分子