Nuclear Physics

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Nuclear physics is the study of the nucleus. The nucleon model is a successful model wherein the smallest fundamental elements of nucleus are the proton and neutron. Although it is now known that protons and neutrons can be built up from smaller elements called quarks, the nucleon model works very well to describe nuclear reactions and interactions.

The force that binds nucleons together into the nucleus is called the strong nuclear force, or simply the strong force. It is the most powerful known force, although it has a limited range. The balance between the strong force and the electromagnetic force(and also the weak nuclear force, not discussed in physics 102) that determine the stability and types of decays in nuclei.

Binding Energy

The famous equation describing mass-energy equivalence is $E=mc^{2}$. On macroscopic scales, masses of systems are mostly constant and mechanical energies of systems are typically much smaller than the energy-equivalent of the masses involved. For this reason mass-energy equivalence is not usually an important factor to consider when describing systems. As an example, consider that the energy equivalence of a 1 kilogram object (the mass of an average textbook) is $9\times 10^{16}J$. In order for the same object to have that much kinetic energy, it would need to be traveling faster than the speed of light.

However, on nuclear scales, mass-energy equivalence is an important factor since the typical energies of interactions are comparable to the mass-energies of the objects involved.

Consider the deuterium nucleus, which is composed of one proton and one neutron. The measured masses of a deuterium nucleus ($m_{d}$), a proton ($m_{p}$) and a neutron ($m_{n}$), are:

$m_{d}=2.0141u$

$m_{p}=1.0073u$

$m_{n}=1.0087u$

where $u$ is the atomic mass unit, defined to be one twelfth the mass of carbon 12, or $1.6605\times 10^{-24}kg$.

We see that the total mass of a proton and a neutron is $2.0160u$, slightly less than the mass of a deuterium nucleus. We can calculate the energy equivalent of this difference in mass:

$E=\Delta mc^{2}=(2.0160u-2.0141u)(931.5{\frac {MeV/c^{2}}{u}})=42.7559MeV/c^{2}$

This energy is often called the mass defect or binding energy of the nucleus. Like compressing a string, squishing neutrons and protons together requires energy because of the repulsive forces they apply on each other. This energy is stored as binding energy and is subtracted from the mass energy of each part. In the process of nuclear fission, nuclei are split apart, which releases this stored energy.

Radioactive Decay

When the strong force is overcome by the repulsive forces between nucleons, nuclei undergo various types of decay. The three major types are alpha, beta, and gamma decay.

Alpha Decay is characterized by the release of a helium nucleus (2 neutrons and 2 protons) from an unstable parent nuclei. For example, Uranium-238 (a radioactive element) may spontaneously emit an alpha particle (i.e. a helium nucleus) to yield the element Thorium-234. Alpha decay most often occurs in nuclei of relatively high mass, due to the relative instability in such nuclei (due to low binding energy) whereas alpha particles are highly stable (the binding energy is relatively high).

Beta Decay is characterized by the release of a beta particle which may be either an electron (designated as β^-) or positron (β⁺). As such, beta decay results in the change of atomic number by 1 but only a slight change of atomic mass (much less than one). Often, beta negative decay occurs in nuclei with a high proportion of neutrons while beta positive decay may occur in nuclei with a higher proportion of protons. Electron capture is closely related to beta decay (i.e. positron emission) although the mechanism is slightly different (it is more similar to beta negative decay).

Gamma decay is characterized by the release of gamma radiation. A nuclei in an excited state is designated by an asterisk (*). No atomic mass or number change results after emittance of the radiation.