1. The problem statement, all variables and given/known data An atom of mass M is initially at rest, in its ground state. A moving (nonrelativistic) electron of mass m_e collides with the atom. The atom+electron system can exist in an excited state in which the electron is absorbed into the atom. The excited state has an extra, "internal," energy E relative to the atom's ground state. To be honest, I am very confused reading this. The problem system I am going through has a section where you can ask for hints and for the most part that's mostly how I've been trying to complete this, but a more clear explanation of what this is saying would be helpful. 2. Relevant equations Kinetic energy = 1/2 mv^2 Momentum = mv 3. The attempt at a solution Well using the hints, first I was asked to find the final velocity of the atom, supposing the initial velocity was v_0. So using conservation of momentum I found it. Here's the work I did so far: So I eliminated it and got K final = (Kinitial * m_e) / (m_e + M) But where to go from here? I tried for a long time but I don't understand this problem at all. The answer given is this: K_e = ([M + m_e] / M) * E Can someone please tell me how they got this answer? As you can see I don't need the answer, I just want to understand this problem~! The most confusing aspect to me is what this E is supposed to represent, where it comes in, I don't get it..