Final answer:
The electron will be traveling at approximately 2.19 x 10^7 m/s.
Step-by-step explanation:
To determine how fast an electron will be traveling after falling to within 1x10-10 m of a proton, we can use the principle of conservation of energy. The electron starts with zero potential energy at infinity and will gain kinetic energy as it falls towards the proton. At a distance of 1x10-10 m, the proton and electron will have equal and opposite electric potential energy.
Using the equation for electric potential energy, we can set the initial potential energy equal to the final kinetic energy, and solve for the electron's final velocity. The final velocity of the electron will be approximately 2.19 x 107 m/s.