If the two charges are far apart initially (\(\displaystyle r >> r_1 + r_2\)), then we can say that the initial potential energy is zero.

\(\displaystyle U_0 = 0\)

If the proton is "just" penetrating the unknown element, it is situated in its electric field and must gain a potential energy equal to:

\(\displaystyle U_1 = \frac{q Q}{4 \pi \epsilon_0 (r + R)}\)

Therefore, the energy that needs to be bestowed to the proton is equal to

\(\displaystyle \Delta U = U_1 - U_0 = \frac{q Q}{4 \pi \epsilon_0 (r + R)}\)

The definition of the potential difference is the work done by an electric field per Coulomb of charge operated on. In other words,

\(\displaystyle V = \frac{W}{q}\)

We can set \(\displaystyle W = \Delta U\), so we get

\(\displaystyle V = \frac{\Delta U}{q} = \frac{Q}{4 \pi \epsilon_0 (r + R)}\)