The electric potential energy of two protons is 1.0MeV. Calculate their separation

First thing first, we need to fully understand what we are asked and what topic we are being tested on. From this question, we can see that we are involved in electric fields, sicne we can see the "electronic potential energy" and"protons" phrases or words. Next, we need to identify what is asked and what is given. In this question, we are given that V = 1.0MeV and we are asked to calculate their separation which is the distance between the two protons. Next, we need to think which tools can we use to answer this question, so we can think of equations in this case, since it's a calculation type question. The best and recommended way to find the appropriate equation is to use your formula sheet to navigate to Electric Fields in this case, your data and what is asked to find out. In this example, we are lucky enough to use one equation to solve this problem which is E = Qq/4πε₀r. 

Before tackling this problem, we need to check whether we need to convert any units into base units (such as s,m,J,A,C etc). In this case, we are given E (EPE) in MeV. So we are going to convert it into joules (J).

So we have: E=1.6 x 10^-19 x 1.0 x 10⁶ = 1.6 x 10^-13J

Where M = 10⁶ (Mega)

Now, we are going to use the formula we have identified earlier to solve the problem. We need to rearrange the formula to make 'r' the subject, since will make things simpler. So, we have:

E = Qq/4πε₀r <=> 4πε₀rE = Qq <=> r = Qq/4πε₀E

Next, we subtitute the values we are given. You know the charge of the protos (Q,q = 1.6 x 10^-19C equal to the electron's charge) and the relative permitivity of a substance constant (8.85 x 10^-12Fm^-1).

By using those data, you have everything to solve this problem and getting an answer. By plugging in to the calculator, we get:

r = (1.6 x 10^-19)²/(4 x π x 8.85 x 10^-12 x 1.6 x 10^-13) = 1.44 x 10^-15m

Hence the separation distance between the two protons is r = 1.44 x 10^-15m