You have always wondered exactly how strong is the interaction called the strong nuclear interaction, and you suspect that an element like uranium could make a good test case. You begin to wonder if the electric potential energy discussed in this chapter might provide a path to an answer. As you search for a starting point, you return to Example 25. 4, which examines the energy associated with holding the hydrogen atom together. But there is only one proton in the hydrogen nucleus, whereas a uranium nucleus has 92 protons, separated from one another by about \(2 \times 10^{-15} \mathrm{~m}\). Clearly something must be able to hold all those protons so close to one another. How strong is this interaction?

Data from Example 25. 4

A (simplistic) model of the hydrogen atom treats the electron as a particle carrying a charge \(-e\) orbiting a proton (a particle carrying a charge \(+e\) ) in a circle of radius \(r_{\mathrm{H}}=0.53 \times 10^{-10} \mathrm{~m} .\) 

(a) How much energy is required to completely separate the electron from the proton? For simplicity, ignore the electron's kinetic energy. 

(b) Across what potential difference does the electron travel as it is separated from the proton?