Question

Using the concept of magic numbers, explain why alpha emission is relatively common, but proton emission is nonexistent.

Short answer

Alpha emission is relatively common because the emission of an alpha particle (consisting of 2 protons and 2 neutrons) results in a significant improvement in nuclear stability due to the high binding energy of alpha particles and their magic numbers. However, proton emission is nonexistent because the emission of a single proton does not lead to a significant gain in nuclear stability, and the energy to overcome the strong nuclear force is too high for this decay process to occur.

Step-by-step solution

Understanding Magic Numbers

Magic numbers are specific numbers of protons or neutrons in an atomic nucleus that result in a more stable and less reactive configuration. These magic numbers are 2, 8, 20, 28, 50, 82, and 126. When an atomic nucleus has a magic number of protons or neutrons, it is particularly stable and resistant to decay.

Stability of Nuclei

The stability of an atomic nucleus depends on the balance between the attractive strong nuclear force, which holds protons and neutrons together, and the repulsive electrostatic force between protons. More stable nuclei have a lower overall energy state, and they are less likely to decay spontaneously. Nuclei with filled energy levels are more stable than those with unfilled levels. This is because filled levels result in maximum binding energy, reducing the probability of decay.

Alpha Emission

Alpha emission is a common radioactive decay process where an unstable nucleus emits an alpha particle consisting of 2 protons and 2 neutrons (a helium-4 nucleus). This process results in a lighter nucleus with a lower atomic number. The reason alpha emission is relatively common is because of the high binding energy of alpha particles. When an alpha particle is emitted, the remaining nucleus has more tightly bound nucleons, which leads to a lower overall energy state, making the nucleus more stable.

Proton Emission

In contrast, proton emission is the process in which a single proton is emitted from an unstable nucleus. This is a theoretical decay process that, if it were to occur, would result in a lighter nucleus with a lower atomic number. However, proton emission is nonexistent because the emission of a single proton does not result in a significant gain in nuclear stability.

Comparing Alpha and Proton Emission

The primary reason that alpha emission is common while proton emission is nonexistent is due to the differences in nuclear stability gained from these decay processes. Alpha emission results in a much greater improvement in nuclear stability than proton emission because the alpha particle has a particularly stable configuration with a magic number of both protons and neutrons (2). In the case of proton emission, the stability gain from emitting a single proton is not significant enough to compensate for the energy required to overcome the strong nuclear force, making this decay process highly unlikely.