Determine the maximum Coulomb force that can act on the electron...

The Coulomb force between the nucleus and the electron in a hydrogen atom is given by:

$F = \dfrac{1}{4\pi\epsilon_0} \dfrac{e^2}{r^2}$

For the force to be maximum, the distance $r$ between the electron and the nucleus must be minimum. This occurs in the first orbit ($n=1$), where the radius is the Bohr radius $r = 0.529 \times 10^{-10}\text{ m}$.

Substituting the standard values:

F_\max = \dfrac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{(0.529 \times 10^{-10})^2}

F_\max = \dfrac{9 \times 10^9 \times 2.56 \times 10^{-38}}{0.2798 \times 10^{-20}}

F_\max = 82.3 \times 10^{-9}\text{ N} \approx 8.2 \times 10^{-8}\text{ N}