2.4 PHYSICAL CONSTANTS USED AS ATOMIC UNITS

Sometimes fundamental physical constants, or other well defined physical quantities, are used as though they were units in certain specialized fields of science. For example, in astronomy it may be more convenient to express the mass of a star in terms of the mass of the sun. In atomic and molecular physics it is similarly more convenient to express masses in terms of the electron mass, $m_{\rm{e}}$, or in terms of the unified atomic mass unit, $1\ \rm{u}$, and to express charges in terms of the elementary charge $e$, and energies in terms of the electronvolt, $\rm{eV}$.

The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of $1\ \rm{V}$ in vacuum, $1\ \rm{e}V = 1.602\ 176\ 634 \times 10^{−19}\ \rm{J}$. The numerical value of a quantity expressed in this unit may be converted into its value when expressed in the SI by multiplication with the value of the physical constant in the SI.

The dalton and the unified atomic mass unit are alternative names for the same unit, therefore $1\ \rm{u} = 1 \rm{Da} \approx 1.6605 \times 10^{−27}\ \rm{kg}$. The dalton may be combined with the SI prefixes to express the masses of large molecules in kilodalton ($\rm{kDa}$) or megadalton ($\rm{MDa}$).

Physical quantity	Physical constant	Symbol for unit	Value in SI units	Notes
mass	electron mass	$m_{\rm{e}}$	$\approx 9.1094 \times 10^{-31}\ \rm{kg}$
charge	elementary charge	$e$	$= 1.602\ 176\ 634 \times 10^{-19}\ \rm{C}$
action, (angular momentum)	Planck constant divided by $2\pi$	$\hbar$	$= 1.054\ 571\ 817 \times 10^{-34}\ \rm{J s}$	1
length	bohr	$a_{0}$	$\approx 5.2918 \times 10^{-11}\ \rm{m}$	1
energy	hartree	$E_{\rm{h}}$	$\approx 4.3597 \times 10^{-18}\ \rm{J}$	1
time		$\hbar/E_{\rm{h}}$	$\approx 2.1489 \times 10^{-17}\ \rm{s}$
speed		$a_{0}E_{\rm{h}}/\hbar$	$\approx 2.1877 \times 10^{6}\ \rm{m\ s}^{-1}$	2

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(1) $\hbar = h/2\pi; a_{0} = 4\pi \varepsilon_{0} \hbar^2/m_{e}e^2; E_{\rm{h}} = \hbar^2/m_{e}a_{0}^2$.