In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass, e is the charge on the electron and ε₀ is the vacuum permittivity, the speed of the electron is

$\frac{e}{\sqrt{4 \pi \varepsilon_0 a_0 m}}$

$\frac{m v^2}{a_0}=\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{a_0^2} \Rightarrow v=\frac{e}{\sqrt{4 \pi \varepsilon_0 a_0 m}}$