diatomic adj : of or relating to a molecule made up of two atoms; "a diatomic molelcule"
- (of a molecule etc) consisting of two atoms
- 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 \,
- \mu \, is the reduced mass
of the molecule and
- r_ \, is the average distance between the two atoms in the molecule.
- \mu \, is the reduced mass of the molecule and
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,... \,
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:
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