Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
In Rutherford hit nitrogen-14 with alpha particles and made oxygen-17 and a proton. The atomic masses are u for nitrogen-14, u for helium-4, u for oxygen-17 and u for hydrogen-1. Find the Q value of the reaction. Find the least kinetic energy that the alpha particles must have, if the nitrogen is at rest.
In a nuclear reaction the total mass number and the total charge stay the same. The energy released is , with atomic masses. For a target at rest, the threshold energy of an endothermic reaction is . From rest, two products share the energy in the inverse ratio of their masses.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The masses. Before: u. After: u.
Step 2. The Q value. The mass before minus the mass after is u. So MeV. The products are heavier, so the reaction is endothermic.
Step 3. The threshold. MeV.
Answer: MeV, and the alpha particles need at least MeV.
Check. The alpha particles from natural sources have MeV or more, so they can start the reaction. The threshold is higher than , as it must be.
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