The deuterium nucleus starts out with a kinetic energy of 9.6e-14 joules, and th
ID: 1535534 • Letter: T
Question
The deuterium nucleus starts out with a kinetic energy of 9.6e-14 joules, and the proton starts out with a kinetic energy of 1.92e-13 joules. The radius of a proton is a 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch? K_1_m + K_2_n = 1.6e-13 joules B: Reaction to make helium Now that the proton and the deuterium nucleus are touching, the reaction can occur. Take the final state from the previous process to be the initial state of the system for this new process. Which diagram depicts the final state? b c a Compare the initial state and final states of the system. Which quantities have changed? rest energy kinetic energy potential energy What is the kinetic energy of the reaction products (helium nucleus plus photon)? K_N_ Element + K, = joules C: Gain of kinetic energy: What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?) Delta K = joules D: Fusion as energy source Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated? joulesExplanation / Answer
I think you might have gotten the problem statement mixed up, a Hydrogen nucleus is just a proton, a Deuterium nucleus is a proton and a neutron. When you combine those, you're still short a neutron to make the Helium nucleus which is 2 protons and 2 neutrons (Unless you're talking about multiple dueterons and multiple protons colliding at once, but that is very unlikely).
You might think that the kinetic energy of the reactants is what gets converted into mass and that can make the extra neutron, but no. I don't know if your reaction is specifically forbidden by any particular law of physics, but the energy levels required to do it are enormous (much bigger than the energy levels that you're considering here).
Usually in a nuclear reaction the mass discrepancy is not in the form of whole protons or neutrons, but just in what's called the binding energy of the atoms. You'll notice that the mass of a Helium nucleus isn't quite exactly the same as the sum of the masses of 2 protons and 2 neutrons, it is these tiny deviations that make up the discrepancies in nuclear reactions.
For example, in the sun Hydrogen is fused into Helium, the reaction there is Tritium+Deuterium -> Helium+loose neutron+energy. There, you go from 2 protons and 3 neutrons to 2 protons and 3 neutrons. This is probably the most common fusion reaction that people talk about. Notice that the mass discrepancy in it is way, way less than 1a.m.u, which is what you would be looking at in the problem that you describe