**Atomic birimler**(Atomic units) (

**au**veya

**a.u.**) form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units,

**Hartree atomic units**and

**Rydberg atomic units**, which differ in the choice of the unit of mass and charge. This article deals with

**Hartree atomic units**. In atomic units, the numerical values of the following four fundamental physical constants are all unity by definition: * electron mass $\backslash !m\_\backslash mathrm$; * elementary charge $\backslash !e$; * reduced Planck's constant $\backslash hbar\; =\; h/(2\; \backslash pi)$; * Coulomb's constant $1/(4\; \backslash pi\; \backslash epsilon\_0)$. Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts. Kullanım ve notasyon Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI. Suppose a particle with a mass of

*m*has 3.4 times the mass of electron. The value of

*m*can be written in three ways: * "$m\; =\; 3.4~m\_e$". This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol. * "$m\; =\; 3.4~\backslash mathrm$" ("a.u." means "expressed in atomic units"). This notation is ambiguous: Here, it means that the mass

*m*is 3.4 times the atomic unit of mass. But if a length

*L*were 3.4 times the atomic unit of length, the equation would look the same, "$L\; =\; 3.4~\backslash mathrm$" The dimension needs to be inferred from context. Temel atomik birimler These four fundamental constants form the basis of the atomic units (see above). Therefore, their numerical values in the atomic units are unity by definition. || |- | charge || elementary charge || $\backslash !e$ || |- | angular momentum || reduced Planck's constant ||$\backslash hbar\; =\; h/(2\; \backslash pi)$ || |- | electric constant || Coulomb force constant ||$1/(4\; \backslash pi\; \backslash epsilon\_0)$ || |} İlgili fiziki sabitler Dimensionless physical constants retain their values in any system of units. Of particular importance is the fine-structure constant $\backslash alpha\; =\; \backslash frac\; \backslash approx\; 1/137$. This immediately gives the value of the speed of light, expressed in atomic units. =\frac\frac c^2} || $\backslash !\backslash alpha^2\; \backslash approx\; 5.32\backslash times10^$ |- | proton mass || $m\_\backslash mathrm$ || $m\_\backslash mathrm/m\_\backslash mathrm\; \backslash approx\; 1836$ |- |} Derived atomic units Below are given a few derived units. Some of them have proper names and symbols assigned, as indicated in the table.

*k*

_{B}is Boltzmann constant. e^2) = \hbar / (m_\mathrm c \alpha) || || = |- | energy || Hartree energy || $\backslash !E\_\backslash mathrm$ || $m\_\backslash mathrm\; e^4/(4\backslash pi\backslash epsilon\_0\backslash hbar)^2\; =\; \backslash alpha^2\; m\_\backslash mathrm\; c^2$ || || = |- | time || || || $\backslash hbar\; /\; E\_\backslash mathrm$ || || |- | velocity || || || $a\_0\; E\_\backslash mathrm\; /\; \backslash hbar\; =\; \backslash alpha\; c$ || || |- | force || || || $\backslash !\; E\_\backslash mathrm\; /\; a\_0$ || ||= |- | temperature || || || $\backslash !\; E\_\backslash mathrm\; /\; k\_\backslash mathrm$|| || |- | pressure || || || $E\_\backslash mathrm\; /\; ^3$ || || |- |electric field || || || $\backslash !E\_\backslash mathrm\; /\; (ea\_0)$ || || = |- |electric dipole moment || || || $e\; a\_0$ || || |} SI and Gaussian-CGS variants, and magnetism-related units There are two common variants of atomic units, one where they are used in conjunction with SI units for electromagnetism, and one where they are used with Gaussian-CGS units. Although the units written above are the same either way (including the unit for electric field), the units related to magnetism are not. In the SI system, the atomic unit for magnetic field is : 1 a.u. = $\backslash frac$ = T = G, and in the Gaussian-cgs unit system, the atomic unit for magnetic field is : 1 a.u. = $\backslash frac$ = T = G. (These differ by a factor of α.) Other magnetism-related quantities are also different in the two systems. An important example is the Bohr magneton: In SI-based atomic units, : $\backslash mu\_B\; =\; \backslash frac\; =\; 1/2$ a.u. and in Gaussian-based atomic units, : $\backslash mu\_B\; =\; \backslash frac=\backslash alpha/2\backslash approx\; 3.6\backslash times\; 10^$ a.u. Atomik birimde Bohr modeli Atomic units are chosen to reflect the properties of electrons in atoms. This is particularly clear from the classical Bohr model of the hydrogen atom in its ground state. The ground state electron orbiting the hydrogen nucleus has (in the classical Bohr model): * Orbital velocity = 1 * Orbital radius = 1 * Angular momentum = 1 * Orbital period = 2π * Ionization energy = * Electric field (due to nucleus) = 1 * Electrical attractive force (due to nucleus) = 1 Non-relativistic quantum mechanics in atomic units The Schrödinger equation for an electron in SI units is : $-\; \backslash frac\; \backslash nabla^2\; \backslash psi(\backslash mathbf,\; t)\; +\; V(\backslash mathbf)\; \backslash psi(\backslash mathbf,\; t)\; =\; i\; \backslash hbar\; \backslash frac\; (\backslash mathbf,\; t)$. The same equation in

**au**is : $-\; \backslash frac\; \backslash nabla^2\; \backslash psi(\backslash mathbf,\; t)\; +\; V(\backslash mathbf)\; \backslash psi(\backslash mathbf,\; t)\; =\; i\; \backslash frac\; (\backslash mathbf,\; t)$. For the special case of the electron around a hydrogen atom, the Hamiltonian in SI units is: : $\backslash hat\; H\; =\; -\; \backslash nabla^2\}\; -\; \}$, while

**atomic units**transform the preceding equation into : $\backslash hat\; H\; =\; -\; \backslash nabla^2\}\; -$. Comparison with Planck units Both Planck units and au are derived from certain fundamental properties of the physical world, and are free of anthropocentric considerations. It should be kept in mind that au were designed for atomic-scale calculations in the present-day universe, while Planck units are more suitable for quantum gravity and early-universe cosmology. Both au and Planck units normalize the reduced Planck constant. Beyond this, Planck units normalize to 1 the two fundamental constants of general relativity and cosmology: the gravitational constant

*G*and the speed of light in a vacuum,

*c*. Atomic units, by contrast, normalize to 1 the mass and charge of the electron, and, as a result, the speed of light in atomic units is a large value, $1/\backslash alpha\; \backslash approx\; 137$. The orbital velocity of an electron around a small atom is of the order of 1 in atomic units, so the discrepancy between the velocity units in the two systems reflects the fact that electrons orbit small atoms much slower than the speed of light (around 2 orders of magnitude slower). There are much larger discrepancies in some other units. For example, the unit of mass in atomic units is the mass of an electron, while the unit of mass in Planck units is the Planck mass, a mass so large that if a single particle had that much mass it might collapse into a black hole. Indeed, the Planck unit of mass is 22 orders of magnitude larger than the au unit of mass. Similarly, there are many orders of magnitude separating the Planck units of energy and length from the corresponding atomic units. See also * Planck units * Natural units * Various extensions of the CGS system to electromagnetism. References * External links * CODATA Internationally recommended values of the Fundamental Physical Constants.