Bohr radius

Niels Bohr's theory (1913) of the hydrogen atom predicts a smallest orbit for the electron circulating the hydrogen nucleus. Today the radius of this orbit is called the Bohr radius. It is usually indicated by a₀. In the old quantum theory of Bohr and Arnold Sommerfeld, as well as in the new quantum theory of Werner Heisenberg and Erwin Schrödinger the radius is given by

$a_{0}={\frac {4\pi \epsilon _{0}\hbar ^{2}}{\mu e^{2}}}\approx 0.529\,177\,208\,59\cdot 10^{-10}\;\mathrm {m}$

where ε₀ is the vacuum permittivity (electric constant), $\hbar$ is Planck's reduced constant, μ is the reduced mass of the hydrogen atom (is equal to the electron mass when the proton mass may supposed to be infinite; for the numerical value this is assumed) and e is the charge of the electron.

In quantum mechanics, a₀ appears in the solution of the Schrödinger equation for the hydrogen atom as the maximum in the radial part of the electronic wave function of lowest energy, the maximum in the so-called 1s atomic orbital.

External link

NIST value for bohr radius