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${\displaystyle a_{0}={\frac {4\pi \epsilon _{0}\hbar ^{2}}{\mu e^{2}}}\approx 0.529\,177\,208\,59\cdot 10^{-10}\;\mathrm {m} }$
where ε0 is the vacuum permittivity (electric constant), ${\displaystyle \hbar }$ 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 given this assumption is made) and e is the charge of the electron.