Physics:Hartree
The hartree (symbol: Eh), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222071(85)×10−18 J[1] = .
The hartree is approximately the negative electric potential energy of the electron in a hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections.
The hartree is usually used as a unit of energy in atomic physics and computational chemistry: for experimental measurements at the atomic scale, the electronvolt (eV) or the reciprocal centimetre (cm−1) are much more widely used.
Other relationships
- [math]\displaystyle{ E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\varepsilon_0\hbar}\right)^2 = m_\mathrm{e} c^2 \alpha^2 = {\hbar c \alpha \over {a_0}} }[/math]
where:
- ħ is the reduced Planck constant,
- me is the electron mass,
- e is the elementary charge,
- a0 is the Bohr radius,
- ε0 is the electric constant,
- c is the speed of light in vacuum, and
- α is the fine-structure constant.
Effective hartree units are used in semiconductor physics where [math]\displaystyle{ e^2 }[/math] is replaced by [math]\displaystyle{ e^2/\varepsilon }[/math] and [math]\displaystyle{ \varepsilon }[/math] is the static dielectric constant. Also, the electron mass is replaced by the effective band mass [math]\displaystyle{ m^* }[/math]. The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).[2]
References
- ↑ "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. http://physics.nist.gov/cgi-bin/cuu/Value?hr. Retrieved 2019-05-20.
- ↑ Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)
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