# Debye

Short description: CGS unit of electric dipole moment

The debye (symbol: D) (/dɛˈb/;[1] Dutch: [dəˈbɛiə]) is a CGS unit[2] (a non-SI metric unit) of electric dipole moment[note 1] named in honour of the physicist Peter J. W. Debye. It is defined as 1×10−18 statcoulomb-centimeters.[note 2] Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb[note 3] (generally called e.s.u. (electrostatic unit) in older scientific literature), which were separated by 1 Ångström.[note 4] This gave a convenient unit for molecular dipole moments.

 1 D = 10−18 statC·cm = 10−10 esu·Å[note 2] = ​1⁄299,792,458×10−21 C·m[note 5] ≈ 3.33564×10−30 C·m ≈ 1.1004×1023 qPlP ≈ 0.3934303 e·Bohr[3] ≈ 0.2081943 eÅ ≈ 0.02081943 e·nm

Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric homoatomic species, e.g. chlorine, Cl2, have zero dipole moment, and highly ionic molecular species have a very large dipole moment, e.g. gas-phase potassium bromide, KBr, with a dipole moment of 10.41 D.[4]

The debye is still used in atomic physics and chemistry because SI units are inconveniently large. The smallest SI unit of electric dipole moment is the yoctocoulomb-meter, which is roughly 300,000 D.[note 6] There is currently no satisfactory solution to this problem of notation without resorting to the use of scientific notation.

## Notes

1. Two equal and opposite charges separated by some distance constitute an electric dipole. This dipole possesses an electric dipole moment whose value is given as charge times length of separation ,it is a vector whose direction is in the direction of the unit vector of the position vector of the positive charge w.r.t negative charge:
p = qr.
2. The statcoulomb is also known as the franklin or electrostatic unit of charge.
1 statC = 1 Fr = 1 esu.
3. 10−10 statcoulomb is approximately 0.2083 units of elementary charge.
4. The ångström is of an order of magnitude close to that of a typical covalent bond.
1 Å = 100 pm = 10−8 cm = 10−10 m.
5. One debye equals 1×10−21 C·m2/s divided by the speed of light in vacuum. Conversely, 1 C·m = 2.9979×1029 D.
6. Yocto-, with a value of 10−24, is the smallest SI prefix. Note that SI disallows the application of prefixes to both members of a compound unit or the compounding of prefixes, thus ruling out such units as the femtocoulomb-femtometre or the microyoctocoulomb-metre (both approximately 0.3 D) respectively.

## References

1. "Debye". Random House Dictionary. 2013.
2. CGS units R. Rowlett (University of North Carolina at Chapel Hill).
3. Physical chemistry 2d Edition (1966) G. M. Barrow. McGraw-Hill.