Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A nucleus of radium-226 at rest emits an alpha particle and becomes radon-222. The atomic masses are u for radium-226, u for radon-222 and u for helium-4. Find the energy released. Find the kinetic energy of the alpha particle and the kinetic energy of the radon nucleus. Use , and take the masses of the products as the atomic masses.
In every decay the total mass number and the total charge stay the same. An alpha decay changes by . A beta-minus decay changes it by . The energy released is , with atomic masses: for alpha decay, for beta-minus, and for beta-plus, where MeV. The products share the kinetic 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 lost mass. u.
Step 2. The energy. MeV.
Step 3. The sharing. Momentum is conserved from rest, so . Kinetic energy is , with the same for both. So , and MeV.
Step 4. The radon nucleus. MeV.
Answer: MeV in all, MeV for the alpha particle and MeV for radon.
Check. The shortcut MeV gives the same answer. The alpha particle takes of the energy.
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