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Nevertheless, the Bohr radius formula remains central in atomic physics calculations, due to its simple relationship with fundamental constants (this is why it is defined using the true electron mass rather than the reduced mass, as mentioned above). As such, it became the unit of length in atomic units. In Schrödinger's quantum-mechanical ...
For more recent data on covalent radii see Covalent radius. Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom. The Bohr radius is consequently known as the "atomic unit of length".
The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius.
It is generally considered the average length for a carbon–carbon single bond, but is also the largest bond length that exists for ordinary carbon covalent bonds. Since one atomic unit of length (i.e., a Bohr radius) is 52.9177 pm, the C–C bond length is 2.91 atomic units, or approximately three Bohr radii long.
The radius is then defined to be the classical electron radius, , and one arrives at the expression given above. Note that this derivation does not say that is the actual radius of an electron. It only establishes a dimensional link between electrostatic self energy and the mass–energy scale of the electron.
Bohr calculated that a 1s orbital electron of a hydrogen atom orbiting at the Bohr radius of 0.0529 nm travels at nearly 1/137 the speed of light. [11] One can extend this to a larger element with an atomic number Z by using the expression v ≈ Z c 137 {\displaystyle v\approx {\frac {Zc}{137}}} for a 1s electron, where v is its radial velocity ...
The last expression in the first equation shows that the wavelength of light needed to ionize a hydrogen atom is 4π/α times the Bohr radius of the atom. The second equation is relevant because its value is the coefficient for the energy of the atomic orbitals of a hydrogen atom: E n = − h c R ∞ / n 2 {\displaystyle E_{n}=-hcR_{\infty }/n ...
The van der Waals radius, r w, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals ...