Nuclear Physics

Nuclear physics, as the name implies, deals with the model and mechanics of the nucleus.

Nucleus structure

Building upon the understanding of a central positive charge—called a proton—in the nucleus of hydrogen, it seemed reasonable to assume that other atoms also had nuclei with protons.

Sir James Chadwick demonstrated the existence of a neutral particle—called a neutron—that has essentially the same mass as the proton. The nucleus is made of protons and neutrons that, collectively, are called nucleons. According to the modern model of the nucleus, the atomic number ( Z) is the number of protons in the nucleus, and the atomic mass ( A) is the number of nucleons in the nucleus. (The number of electrons is equal to the number of protons in an electrically neutral atom, and so the number of orbiting electrons is also given by the value of Z.) Nuclei with the same number of protons but differing number of neutrons are called isotopes. The chemical properties of an element are determined by the outer electrons (equal to the number of protons); therefore, isotopes are identical in chemical nature but differ in mass. The symbol for an element ( X) is _Z^AX; for example, ₄ ⁹Be is beryllium with four protons and five neutrons.

Binding energy

When the masses of the constituent particles of a nucleus are added together, the sum is less than the nucleus itself. For example, a deuteron is an isotope of hydrogen with one proton and one neutron in the nucleus. The following below adds these particles in atomic mass units—abbreviated here as amu—where 1 amu is 1/12 of a carbon atom with 12 nucleons.

The observed mass of the deuteron is 2.014102 amu, which is .002388 less than the sum. Using the mass‐equivalence equation, E = mc ², 1 amu corresponds to approximately 931 MeV. Thus, the mass difference is (0.002388 amu)(931 MeV/amu) = 2.224 MeV. This quantity is called binding energy. The binding energy is the difference between the mass energy of the nucleus and its constituent particles. To separate the nucleus into a proton and neutron, energy equal to the binding energy must be added to the system.

Radioactivity

Some nuclei are unstable and spontaneously emit radiation, which is called radioactivity. The radiation is of three types:

Alpha decay, in which the emitted particles are helium nuclei of 2 protons and 2 neutrons

Beta decay, in which the emitted particles are electrons

Gamma decay, in which high energy photons are emitted

The original nucleus is called the parent nucleus, and the nucleus remaining after the decay is called the daughter nucleus. The process of one element changing into another through radioactivity is called transmutation.

If a nucleus emits an alpha particle, it loses two protons and two neutrons; therefore, the daughter nucleus has an atomic mass of 4 less and an atomic number of 2 less than the parent nucleus. An example of alpha decay of uranium is ₉₂ ²³⁸U → ₉₀ ²³⁴Th + ₂ ²He.

If a nucleus emits a beta particle, it loses an electron. Since the mass of the electron is so small compared to that of a proton and a neutron, the atomic mass of the parent nucleus is the same as the daughter nucleus. The atomic number of the daughter nucleus is one greater than that of the parent nucleus. An example of beta decay of bismuth is ₈₃ ²¹²Bi → ₈₄ ²¹²P ₀ + ₋ ⁰ e.

Frequently the daughter nucleus is left in an excited state after either alpha or beta decay. Then the nucleus can give up excess energy by emission of gamma radiation. The following example shows a typical situation where gamma decay occurs: ₅ ¹²B → ₆ ¹²C* + ₋₁ ⁰ e; then, ₆ ¹²C* → ₆ ¹²C + γ, where the asterisks indicate an excited nucleus.

The rules for radioactive decay are based on conservation laws. Examination of the preceding examples reveals that the number of nucleons and the electric charge are conserved; that is, the total on one side of the equation equals the total on the other side of the equation. Other conservation laws that must be observed are those of energy, momentum, and angular momentum.

Half-life

The decay rate ( R) or the activity of a sample of radioactive material is defined as the number of decays per second, given by R = − λ N, where N is the number of radioactive nuclei at some instant and λ is the decay constant.

The half‐life ( T) is defined as the time required for half of a given number of radioactive nuclei to decay. It is different for each type of radioactive element:

The general decay curve for a radioactive sample relating the number of nuclei present at a given time to the original number of nuclei is exponential. The expression is ₀ ¹ n + ₉₂ ²³⁵U → ₅₆ ²⁴¹Ba + ₃₆ ⁹²Kr + 3 ₀ ¹ n. The total rest mass of the products is less than the original rest mass of the original uranium by 220 MeV. This is an enormous amount of energy compared to energy releases in chemical processes and when considering that a relatively modest piece of uranium has so very many nuclei. Nuclear fusion occurs when light nuclei are combined to form a heavier nucleus. The sun is powered by nuclear fusion.

The binding energy is related to stability. When the mass energy of the parent nucleus is greater than the total mass energy of the decay products, spontaneous decay will take place. If the decay products have a greater total mass energy than the parent nucleus, additional energy is necessary for the reaction to occur. Energy is released when light nuclei combine (fusion) and when heavy nuclei split (fission).