The relation between the orbital radius and the electron velocity for a dynamically stable orbit in a hydrogen atom is: (where, all notations have their usual meanings)

In hydrogen atom electrostatic force of attraction $\left(F_e\right)$ between the revolving electrons and the nucleus provides the requisite centripetal force $\left(F_c\right)$ to keep them in their orbits. 

Thus, 

  $$\begin{gathered} F_e=F_c \\ \Rightarrow \frac{m{v}^2}{r}=\frac{1}{4\pi {\epsilon }_0}\frac{e^2}{r^2} \end{gathered}$$

  $$\begin{gathered} \Rightarrow v^2=\frac{e^2}{4\pi {\epsilon }_{0}mr} \\ \Rightarrow v=\sqrt{\frac{e^2}{4\pi {\epsilon }_{0}mr}} \end{gathered}$$