Nuclei

Nuclear Decay

Unstable nuclei, called radioactive isotopes, will undergo nuclear decay to make it more stable. There are only certain types of nuclear decay which means that most isotopes can't jump directly from being unstable to being stable. It often takes several decays to eventually become a stable nucleus. When unstable nuclei decay, the reactions generally involve the emission of a particle and or energy. Half-lives are characteristic properties of the various unstable atomic nuclei and the particular way in which they decay. Alpha and beta decay are generally slower processes than gamma decay. Half-lives for beta decay range upward from 10^-2 sec and, for alpha decay, upward from about 10^-6 sec. Bismuth-209 has the longest half-life of 2x10¹⁹ years. Half-lives for gamma decay may be too short to measure (~ 10^-14 second), though a wide range of half-lives for gamma emission has been reported.

There are five types of nuclear decay:



Alpha Decay - The strong force, despite its strength, has a very short range; it can't even reach from one end of a fair-sized atomic nucleus to the other. If a proton is at the edge of a big nucleus, it can feel the pulling strong force only from the particles in the neighborhood, but there is an electromagnetic force, which tends to push it out, all the way from the other side of the nucleus. There is a sensitive balance between these two competing forces. The nucleus needs not to acquire extra energy to escape; the quantum mechanical effect called tunnelling allows a certain probability of escape through a potential wall. Alpha decay, in which just a small chunk breaks off from the main nucleus, is a rather mild case of fission; in more dramatic examples, the nucleus can break more or less in half. The broken-off chunk most often is packed into a helium nucleus (alpha particle) because it is in a more stable form. Figure 14-06 shows the effect of tunneling through the Coulomb barrier; the nucleus has a small probability of escape to the outside depending on the height and width of the wall.

Figure 14-06 Alpha Decay [view large image]

Beta Decay - The weak interaction is responsible for the instability of "free" neutrons, which decay according to the reaction: n p + e + electron-anti-neutrino with a lifetime about 15 minutes in a process known as beta decay. Neutrons in a nucleus are subject to the protection of the nuclear and the electromagnetic forces from the other nucleons, and they will remain stable provided there are not too many of them. If there are too many, such protection would not be sufficient for all of them to remain stable, and the nucleus would undergo beta decay. Figure 14-07 shows the beta decay process, in which the down quark turns into an up quark (thus changes the neutron to proton) by emitting a W- meson, which decays into an electron and an electron-anti-neutrino.

Figure 14-07 Beta Decay [view large image]

Gamma Decay - In gamma decay, a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation. It happens usually after the transmutation of the nucleus; the end product has to re-arrange the occupancy of energy levels in order to arrive at a more stable state. The number of protons (and neutrons) in the nucleus does not change in this process, so the parent and daughter atoms are the same chemical element. In the gamma decay of a nucleus, the emitted photon and recoiling nucleus each have a well-defined energy after the decay. Figure 14-08a shows the adjustment of energy level by emitting gamma ray after Mg has transmuted into Al.

Figure 14-08a Gamma Decay [view large image]

Although the three types of radiation mentioned above have roughly the same energy of a few Mev, their penetrating power is different as shown in Figure 14-08b (in Buck Rogers shooting style). The difference is due mainly to the mass and charge carried by the radiation. While the alpha ray readily ionizes the few atoms/molecules near the surface of the material, the beta ray with less mass and charge can penetrate deeper. The gamma ray carries no mass and no charge, it depends on direct hit to ionize the atoms/molecules and thus has the most penetrating power.

Figure 14-08b Radiation Penetrating Power [view large image]



• Positron Emission - Positron emission is a type of beta decay, referred to as "beta plus"(ß+ ) or inverse beta decay. In beta plus decay, a proton is converted to a neutron, a positron and a neutrino via the weak interaction. This spontaneous nuclear process releases an amount of energy equal to the energy equivalent of the rest mass that disappears in the process. The positron and neutrino are created in the nucleus at the moment of disintegration. The "endothermic reactions" receives the energy from the nuclear fission. That positron decay is a nuclear process is consistent with the fact that the decay of free protons by positron emission is not observed in nature. On the other hand, the beta decay of free neutrons is a familiar fact. The positron is made of anti-matter and does not last very long in the world of ordinary matter. As soon as the

positron meets an ordinary electron the two particles annihilate and the energy contained in their mass appears as two gamma-rays of 0.5 MeV each, flying off in opposite directions. Positron radioactivity is therefore always accompanied by the emission of gamma rays with an energy of about 0.5 MeV in addition to any other gamma-rays which might be emitted. Example isotopes, which emit positrons are C-11, N-13, O-15 and F-18. These isotopes are used in positron emission tomography (PET). Figure 14-09 shows the transmutation of C-11 into B-11 by positron emission.

Figure 14-09 Positron Emission [view large image]



• Electron Capture - Electron capture is a decay mode for nucleus that will occur when there are too many protons in the nucleus of an atom, and there isn't enough energy to emit a positron. In this case, one of the orbital electrons is captured by a proton in the nucleus, forming a neutron

and a neutrino. Since the proton is essentially changed to a neutron, the number of neutrons increases by 1, the number of protons decreases by 1, and the atomic mass remains unchanged. By changing the number of protons, electron capture transforms the nucleus into a new element. Electron capture is also called K-capture since the captured electron usually comes from the atom's K-shell. Figure 14-10 shows another way of transmuting C-11 into B-11 by electron capture.

Figure 14-10 Electron Capture [view large image]

Type	Emission	Penetrating Power	Example
Alpha Decay	Helium nuclei	1, stopped by skin, very damaging due to ionization	92U238 90Th234 + 2He4 Applicable to nuclei with Z>82, see Figure 14-02
Beta Decay	Electron, high speed	100, penetrates human tissue to ~ 1 cm	53I131 54Xe131 + -1e0 Applicable to nuclei with high neutron-proton ratio
Gamma Decay	Photons, high energy	10000, highly penetrating but not very ionizing	92U238 90Th234 + 2He4 + 2 photon Energy lost from settling within the nucleus after transmutation
Positron Emission	Positron	100	6C11 5B11 + 1e0 Applicable to nuclei with a low neutron-proton ratio
Electron Capture	Neutrino (from inner shell -1e0)	~ Infinite for Neutrino	37Rb81 + -1e0 36Kr81 + neutrino (e) Applicable to nuclei with a low neutron-proton ratio

Table 14-01 Types of Nuclear Decay

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