\begin{aligned} u & = \sqrt{a r_{H}} \\ = \sqrt{\frac{1}{4 π ε_{0}} \frac{1}{m_{e}} \frac{e^{2}}{r_{H}^{2}} r_{H})} \\ = e \sqrt{\frac{1}{4 π ε_{0}}} \sqrt{\frac{1}{m_{e} r_{H}}} \\ = 1, 6 \times 10^{- 19} \times 3 \times 10^{3} \times 4, 55 \times 10^{20} \\ \approx 2, 2 \times 10^{5} m \cdot s^{- 1} \end{aligned}

${\begin{align*} u &=\sqrt{a r_\text{H}}\\ &=\sqrt{ \frac{1}{4 \pi \varepsilon_0} \frac{1}{m_e} \frac{e^2}{r_\text{H}^2} r_\text{H} )} \\ &=e \sqrt{ \frac{1}{4 \pi \varepsilon_0}} \sqrt{\frac{1}{m_e r_\text{H}}} \\ &=1,6\times 10^{-19} \times 3 \times 10^3 \times 4,55 \times 10^{20} \\ &\approx 2,2 \times 10^5 \, \mathrm{m \cdot s^{-1}} \end{align*}}$

Error