An atomic nucleus at rest decays radioactively into an alpha particle and a different nucleus.
Radioactive decay is a process in which an unstable atomic nucleus undergoes a spontaneous transformation to become more stable. One type of radioactive decay is called alpha decay. In alpha decay, the unstable nucleus emits an alpha particle, which consists of two protons and two neutrons. This emission causes the original nucleus to decay into a different nucleus.
To understand how to calculate the energy released in this process, we need to consider the mass and energy balance.
1. Determine the initial mass of the unstable nucleus. This can be obtained from the atomic mass of the parent nucleus. For example, let's assume the initial nucleus is Uranium-238, which has a mass of 238 atomic mass units (u).
2. Determine the final mass of the alpha particle and the new nucleus. An alpha particle consists of two protons and two neutrons, which have a combined mass of approximately 4 atomic mass units (u). The new nucleus will have a different atomic number and atomic mass.
3. Calculate the mass difference between the initial and final states. This can be done by subtracting the final mass from the initial mass. In this example, the mass difference would be (238 u - 4 u) = 234 u.
4. Apply Einstein's mass-energy equivalence equation, E = mc^2, to calculate the energy released during alpha decay. The equation states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared. The speed of light is approximately 3 x 10^8 meters per second (m/s).
Using the mass difference calculated from step 3, we can calculate the energy released using the equation E = (234 u) x (3 x 10^8 m/s)^2.
5. Convert the energy obtained in step 4 to a more convenient unit, such as electron volts (eV) or joules (J). To convert from atomic mass units (u) to electron volts (eV), you can use the conversion factor 1 u = 931.5 MeV/c^2.
By following these steps, you can calculate the energy released in alpha decay and determine the resulting nucleus after the decay process.